The production function for Marty's Frozen Yogurt is given...

The production function for Marty's Frozen Yogurt is given in Problem 2. Marty pays each of his workers $$\$ 80$$ per day. The cost of his other variable inputs is $$\$ 0.50$$ per cup of yogurt. His fixed cost is $$\$ 100$$ per day. a. What is Marty's variable cost and total cost when he produces 110 cups of yogurt? 200 cups? Calculate variable and total cost for every level of output given in Problem 2 . b. Draw Marty's variable cost curve. On the same diagram, draw his total cost curve. c. What is the marginal cost per cup for the first 110 cups of yogurt? For the next 90 cups? Calculate the marginal cost for all remaining levels of output.

The production function for Marty's Frozen Yogurt is given in Problem 2. Marty pays each of his workers $$\$ 80$$ per day. The cost of his other variable inputs is $$\$ 0.50$$ per cup of yogurt. His fixed cost is $$\$ 100$$ per day.
a. What is Marty's variable cost and total cost when he produces 110 cups of yogurt? 200 cups? Calculate variable and total cost for every level of output given in Problem 2 .
b. Draw Marty's variable cost curve. On the same diagram, draw his total cost curve.
c. What is the marginal cost per cup for the first 110 cups of yogurt? For the next 90 cups? Calculate the marginal cost for all remaining levels of output.

Key Concepts

Marginal Cost

Marginal cost refers to the additional cost incurred by producing one more unit of output. It is derived from changes in total cost when output increases and is a key concept for decision-making in production. Understanding marginal cost helps firms determine the most efficient level of production and make pricing decisions that maximize profits.

Cost Curves

Cost curves graphically represent the relationship between cost and output. They include the variable cost curve, total cost curve, and marginal cost curve, among others. These curves are essential tools in microeconomics as they visually illustrate how costs behave at different production levels and facilitate the analysis of economies of scale, cost efficiency, and optimal production decisions.

Total Costs

Total costs combine fixed and variable costs to show the complete cost of production at different output levels. This concept is essential for businesses as it informs decisions regarding pricing, output levels, and profit maximization. Total cost analysis also aids in determining break-even points and evaluating the impact of production changes.

Variable Costs

Variable costs change directly with the level of production. They include costs such as raw materials, labor wages (if paid per unit or output level), and utilities that vary with production volume. This concept is important because it helps businesses understand how costs scale with output and aids in pricing and production decisions.

Fixed Costs

Fixed costs are expenses that do not vary with the level of output; they are incurred regardless of how much is produced. In the context of business, fixed costs include expenditures such as rent, salaries, and equipment, which must be paid even when production is low or zero. These costs play a crucial role in understanding a firm's cost structure.

Production Function

The production function represents the relationship between input factors, such as labor and materials, and the quantity of output produced. It is a fundamental concept in economics that helps in understanding how changes in the input mix can affect the level of production, and it forms the basis for analyzing cost and efficiency in production processes.

Transcript

00:01 We have marty's production function of frozen yogurt in the left -hand column.

00:07 It shows how many cups of frozen yogurt he can produce in a day with different amounts of workers.

00:13 We pay the workers $80 a piece a day, and our other variable inputs cost 50 cents per cup of yogurt.

00:21 And we're supposed to find variable cost and total cost and do a graph and marginal cost.

00:27 So to get variable cost, i've got the labor cost of $80 times the number of workers plus 50 cents for each cup of yogurt produced in other variable inputs.

00:39 So if i do 110 cups of yogurt, then that takes one worker, so that cost $80.

00:47 And then 50 cents for each of the 110 cups would be another 55 for a total variable cost of 135.

00:56 If i don't produce anything, there's no variable cost of my variable cost of no labor, no output would be zero at the top of the column.

01:07 If we do 200 cups, 160 for two workers at $80 each, plus another 100 for the variable resource would give me 260 in variable cost.

01:20 And then i figure my variable cost the same way for my output levels from 270 on up to 3 .30.

01:29 On the right hand side, i've plotted the points for variable cost.

01:35 You can see when outputs 110, my variable cost would be 135.

01:43 When outputs 200, my variable cost is 260 and so on.

01:48 So if i connect those points, i've got a graph of my variable cost.

01:59 My fixed cost is $100 more than variable cost.

02:03 So to get my total cost is $100 more than my variable cost.

02:10 So to get total cost, we're going to add the $100 fixed cost to the variable cost.

02:16 And so even if we don't produce anything, we still have $100 fixed costs.

02:21 So our total cost even at zero would be 100.

02:25 So if we plot that point, that's where our total cost curve starts.

02:31 At 110 cups, the total cost is the 135 in variable plus another 100 brings us to 235.

02:44 When my output is 200, my total cost would be 360.

02:49 When my outputs 270, my total cost is 475.

03:03 When output is 300, the total is 570...

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