David N. gets 3 per week as an allowance to spend any way he pleases. Because he likes only pea

David N. gets 3 per week as an allowance to spend any way...

Key Concepts

Budget Constraint

The budget constraint represents the limited income available to a consumer that restricts the combinations of goods they can purchase. It is a fundamental concept in consumer theory that shows how a consumer must make trade-offs between spending on different items based on their prices and the consumer's total budget.

Consumer Choice Theory

Consumer choice theory studies how individuals decide to allocate their limited income among various goods and services in order to maximize their utility. It involves analyzing preferences, utility functions, and the impact of price changes on consumption decisions, all within the framework of the budget constraint.

Perfect Complements

Perfect complements are goods that are consumed together in fixed proportions, meaning that the consumer derives utility only from consuming the goods in a specific ratio. This concept simplifies decision-making because the consumption of one good is directly tied to the consumption of the other, effectively turning several goods into a single composite commodity in the analysis.

Income and Substitution Effects

Income and substitution effects explain how changes in prices affect a consumer's purchasing decisions. The substitution effect reflects changes in consumption patterns due to a change in the relative prices of goods, while the income effect deals with the change in consumption resulting from the change in the consumer's real income or purchasing power.

Demand Curve

The demand curve illustrates the relationship between the price of a good and the quantity demanded. It is a core concept in microeconomics that helps explain how changes in price, income, and other factors influence the consumer's decision on how much of a commodity to purchase, integrating both the income and substitution effects.

Transcript

00:01 So david n.

00:02 Gets $3 per week as an allowance to spend any way it pleases.

00:07 So because he likes only peanuts, butter, and jelly sandwiches, it spends the entire amount on peanut butter.

00:20 So peanuts butter, he spends everything on peanut butter and jelly.

00:27 So this peanut butter is 0 .05 per ounce.

00:33 And jelly is 0 .0 .5 per ounce.

00:38 10 cents per ounce and bread is provided free are charged by a consignable so bread is free now there it is a particular eater and it makes the sandwiches with exactly one ounce of jelly so one ounce of jelly and two ounces of peanut butter now it sets in his ways and will never change his proportion so he has to have one ounce of jelly and two ounces of peanut butter then the first question says how much peanut butter and jelly would david buy with this three dollar and allowance in the week so first of all you need to know that these goods are complementary goods because you need it needs the peanut butter and the jelly and the bread to make a complete peanut butter jelly sandwich so and complementary goods are the goods that are consumed together by a consumer like the peanut butter jelly and the bread so consuming the single commodity will not add to the utility of to the utility of others so therefore when the price of one of them increases the demand for the complement would decrease because then nobody wants to buy it so the income of the consumer is the total budget that the individual has to spend on the available commodities now moving on since he's given that um he likes to spend condoom peanut butter and jelly sand we're using one ounce of jelly and two ounces of butter that means that the utility and the demand function is giving as perfect compliments now it is assumed that x stands for peanut butter and y stands for jelly so let's okay i'm sorry let's just go by the way it was so this is two peanut butter and this is jelly so let's say let x be peanut butter and y be jelly so it just so it just looks easier so so the utility function with the for the complementary goods will be you is equals to m ian open brackets x comma two y simply because it consumes one of x and two of y so the money income which is m is of three dollars and the price of peanut butter to be five cents and jelly of 10 cents so the budget constraints would be as follows so p of x plus p y of y is equal to m so 0 .05x plus 0 .010 y is equal to 3 so this is equation 1.

03:51 Now since the two goods are using fixed proportions so therefore x is equal to 2y so we need to calculate the demand function so we substitute x equals to 2y in equation 1 and we're going to get 0 .055.

04:05 X plus 0 .10 y is equal to 3 so therefore 0 .05 multiplied by 2y where we see x plus 0 .10 y is equal to 3 and from there 0 .20 y is equal to 3 and we can say that y is equal to 15 so now we can calculate the value of x as x is equal to 2 y so x is equal to 2 y so x is equal to 2 multiplied by 15 and then x is is equal to 30 right so therefore it would buy peanut butter um and so therefore buy peanut butter and 15 ounces of jelly so we can say that it would buy and remember that 30 um remember that x is x stands for peanut butter so it would buy 30 ounces of peanut butter and why stand for jelly so and 15 ounces of jelly so that's the answer so moving on to the second question suppose that the price of jelly were to increase to 0 .15 an ounce so price of jelly went up to 0 .15 an ounce now how much of each commodity would be bought so when the price increases to this and we need to find a quantity the consumer would buy so at the price of jelly increases to 0 .15 it is more costlier than before than the cost for the consumer rights because before the price of jelly was at 10 um 10 cents and now it's 15 cents so it is more expensive so therefore the new budget constraints will be cost to 0 .05x plus 0 .15 y is equal to 3 so now we substitute x is equal to 2y to get the new um the new consumption bundle and that will look like 0 .05 multiply by 2y plus 0 .15 multiplied by y is equal to 3 so now we can say that 0 .25 y is equal to 3 and then y is equal to 12 so now we substitute the value and the x because to 2y so x is equal to 2 multiplied by 12 and you can say that x is equal to 24 so because of the increase in the price of jelly now um it can now consume 24 ounces of peanut butter and 12 ounces of jelly 24 ounces of peanut butter and 12 ounces of jelly so now the next question by how much would should david allowance be increased to compensate for the increase in the price of jelly in parts be so we need to find the increasing amount of its allowance to compensate for the rise in the price of the second question, which we just did.

08:01 So the increase in the price of jelly has cost the consumption to fall, right? so the increase in price of jelly reduces its consumption.

08:22 So therefore, david must be compensated for the sacrifice unit.

08:29 Right so calculate his new allowance to compensation giving a new income level and the change of income level has the change of m we cost to m1 minus m so therefore y multiplied by the change of p price y is equal to m1 minus 3 so y is 15 in this case multiplied by 0 .15 minus 0 .10 cents which is a change is equals to m1 minus 3 so therefore 3 .75 is equal to m1 so that's m1 so therefore is allowance to compensate to be 3 .75 cents so that's the answer now moving on to the next question it says graph the results in part a to c so the graph will basically look like this and this is the y -axis and this is the x -axis then we have 24 we have 30 we have point 60 and then we have point 75 and then here we have point 12 we have point 15 we have point 20 we have point 25 and we have point 30 so giving the answers we have done from the first question to this level third question we can now draw the graph so the point point 20 years going to be touching 60 on the x -axis and then point 30 is touching the same points 60 so that's that and 25 is touching 75 so this goes all the way to 75 so now that we have that this is the i c2 and then i'm sorry okay so at this middle point is well it's supposed to draw it right here so this is supposed to be ic1 and then the other point is touching this point right here and then this is the ic2 and then from year to year ie so this is the result from the of the graph for the four questions a to c so moving on in what sense does this problem involve any only a single commodity, peanut butter and jelly sandwiches.

12:19 Graph the demand call for this single commodity.

12:25 So we are to graph the demand call for the single commodity and the peanut butter and jelly are complement that are consumed together in bread.

12:34 So peanut butter and jelly are complement for bread.

12:49 So therefore the consumption of bread is the consumption of a single commodity because peanut butter and jelly depend on bread but you can take bread on its own so the consumption of bread is a single commodity and that means that the units of bread consumed will stay fixed given the ounces of butter and jelly used so demand curve that shows the relationship between price and the units of consumption patterns would be um would be the one i'm about to draw below so so, demand curve and this shows the relationship between price and units.

13:42 So our quantity we and the price of bread will be right here...

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