Marty’s Frozen Yogurt is a small shop that sells cups of frozen yogurt. Marty ow
ID: 1162510 • Letter: M
Question
Marty’s Frozen Yogurt is a small shop that sells cups of frozen yogurt. Marty owns three frozen-yogurt machines. His other inputs are refrigerators, frozen-yogurt mix, cups, sprinkle toppings, and, of course, workers. He estimates that his daily production function when he varies the number of workers employed (and at the same time, of course, yogurt mix, cups, and so on) is as shown in the table below. 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. The market price for yogurt is $3 per cup.
What are the fixed inputs and variable inputs in the production of cups of frozen yogurt?
Complete the chart below and answer the following questions.
Why does marginal product decline as the number of workers increases?
What is Marty’s variable cost and total cost when he produces 110 cups of yogurt? 200 cups?
How many cups of frozen yogurt are produced when average total cost is minimized?
Explain why the AFC declines as output increases?
Explain why the AVC increases as output increases?
What is the marginal cost per cup for the first 110 cups of yogurt? 200 cups?
Explanation / Answer
(a) Fixed Inputs: These are those inputswhose quantities do not change as the quantity of output changes. These are frozen-yogurt machines, refrigerators and the shop.
Variable inputs : These are those inputs whose quantity changes as the quantity of output changes. These are Frozen-yogurt mix, cups,sprinkle toppings and workers.
(b) The marginal product of labor declines as the number of workers increases because of the principle of diminishing returns to labor. Since the number of frozen-yogurt machines is fixed , therefore, as the workers added there are fewer and fewer machines available for each worker to work with, which makes each worker less and less productive.
(c) By applying these formulae , we get the table as shown below:
VC = (80)(No. of workers) + (0.50)(Quantity of yogurt)
TC = FC + VC
MC = Change in TC/ Change in Q
Marty's Variable cost when he produces 110 cups of yogurt = $135
Total cost when he produces 110 cups of yogurt = $235
And Marty's variable cost when he produces 200 cups of yogurt = $260.
And Total cost when he produces 200 cups = $360
(d) Average total cost is minimised when 270 cups of yogurt are produced. We can see it by calculating , ATC = TC/Q.
(e) AFC declines as output increases due to spreading effect . The fixed cost is spread over more and more units of output as output increases.
(f) AVC increases as output increases due to diminishing returns effect. That is due to diminishing returns to labor, it costs more to produce each additional unit of output.
(g) MC for the first 110 cups of yogurt = $ 1.23
MC for the first 200 cups of yogurt = $ 1.39
Quantity of labor (workers) Quantity of frozen yogurt (Cups) 0 0 1 110 2 200 3 270 4 300 5 320 6 330Related Questions
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