Question 17 of 23 Sizing Up the Economy Using GDP

Question 17 of 23 Sizing Up the Economy Using GDP — End of Chapter Problem Vinny and Sandra have just had their first baby and must decide how to handle work and child-care responsibilities. Vinny earns $1,000 per week working full time, and Sandra's full-time salary is $1,200 per week. They earn their full-time wages. Calculate the change in GDP for each situation, relative to when they both took time off for child-care responsibilities. If GDP falls, include a negative sign in your answer. a. Both Vinny and Sandra return to work full-time and pay a child-care provider $900 per week. $ b. Both Vinny and Sandra will return to work full-time, while Sandra's mother takes care of the baby without compensation. $

Transcript

00:01 Suppose that there are two types of households in an economy.

00:06 One is called m and other as w.

00:10 Both types live for two periods and have the same utility function and discount rates.

00:15 So we have m and w and same utility and discount rates at i equal to 0 .1 but may differ in the endowments and consumption allocation.

00:24 There is an equal population of each type in m and w.

00:29 The market clearing condition is determined by the interaction of households and the firm or the government.

00:35 The utility maximization problem for the household type 1 and type 2, type 1 is given to us.

00:45 We have to define what will be the competitive equilibrium in this economy and secondly we have to solve for the inter -temporal eurall equation for the household of the type 1.

00:57 Third we have to solve for the consumption allocation in the period 1st and 2nd for the households of the type 1 as a function of their income and the prices.

01:06 And for d we have to suppose that the endowments are given and we have to use the household euler condition and market clearing condition to solve for the market clearing interest rate in this economy.

01:19 Next we have to substitute the market clearing interest rate back into the consumption function from the part c.

01:28 Then the question asks what does household m have, why does the household m have the higher consumption in each period.

01:40 Then if the midwest open up a trade with the rest of the world and act as a small economy, this means two things, open and the small.

01:53 And how does the definition of the competitive equilibrium changes.

01:57 For the h part we have to calculate the consumption allocation for consumer of each type in the small open economy and lastly what will be the net export for the midwest in the each period.

02:08 So, we can as you can see there are lots of parts in this question.

02:11 Let's start with the let's start with the part a.

02:17 The competitive equilibrium in this economy.

02:26 So, the competitive equilibrium the allocation of goods and prices are determined such that all households and the firm maximizes their respective objective and market clears.

02:36 For the household the utility maximization problem for household for the type one which is m or w is given as max log c c1i plus log of c2i subject to c1i plus c2i equals y1i plus y2i.

03:21 For each type of household the problem can be written as can be rewritten as max of log c1m plus log c2m subject to c1w plus c2w equals yw1 plus yw2.

03:59 Moving on with the second part where we have to go forth the intertemporal euler equation for the household of the type one which is m or w.

04:11 Setting up the lagrangian for the household of type one we have the equation as l equals log of c1i plus log of the c2i minus the lambda 1 c1i plus the c2i minus y1i minus y2i.

04:39 Taking the first order conditions with respect to the c1i and the c2i we have the equations as 1 upon c1i minus the lambda 1 equals to 0 for the first equation and 1 upon c2i minus the lambda i equals to 0 for the second equation.

05:06 Combining the these two first order conditions we have the equation as 1 upon c1i equals 1 upon c2i from 1 and second.

05:19 This implies that the intertemporal euler equation for the household of type one where the marginal rate of substitution between the goods today and the goods tomorrow for household i is equal to the inverse of the price ratio which is equal to 1 in this case.

05:35 For the third part of the situation with the consumption allocation in period 1 and 2 for household of type 1 using the burden constraint of which is given to us as c1i plus c2i equals to y1i plus y2i.

05:55 We can solve the consumption allocation in period 1 and 2 for each household in type.

06:04 For household m the c1m equals ym1 minus c2m and for the c2m equals ym2 minus c1m.

06:18 Now for the household w we have c1w equals yw1 minus c2w and similarly c2w equals yw2 minus c1w.

06:33 This is it for this part.

06:35 For the d part we have to calculate the market clearing interest rate.

06:42 We have the endowments ym1 equals 2, ym2 equals 1, yw1 equals 1, yw2 equals 2 and change equals 0 .8.

07:00 We can use the household euler conditions and making a clearing condition to solve the market clearing interest rate in this economy.

07:08 Using the euler equation we have equations as 1 upon c1m equals change in 1 upon c2m and 1 upon c1w equals change in 1 upon c2w...

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