Econ 2000 - Problem Set 4

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Jan 9, 2024

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Econ 2000 Problem Set 4 Name: 1. The production function of pizzas for Top Guy’s Pizza shop is y ( K, L ) = 4 √ KL represents the number of ovens Top Guy’s Pizza uses and is fixed in the short-run at 4 ovens. L represents the number of labor hours One Guy’s Pizza employees and is variable in the short and long-run. Fill in the empty columns in the table below. Pizzas K L MP L = 2 √ K √ L MP K = 2 √ L √ K 4 1 4 4 4 9 4 16 2. You are given the following table for a production process which has two variable outputs. (a) What returns to scale does the production function exhibit? What can be said of the MRTS? (hint: calculate the MRTS for various level of output at 60, 70 85, 95, 105 and 115) (b) Analyze the marginal productivity of labor and capital for the production function. Econ 2000 Problem Set 4 1 / 2

Econ 2000 Problem Set 4 3. Macklem’s Printing production function is given by y ( K, L ) = 2 √ KL where K is the number of capital she uses and L is the number of labor hours. Does this production process exhibit increasing, constant or decreasing returns to scale? Holding the number of vats constant at 4, is the marginal product of labor increasing, constant or decreasing as more labor is used? 4. Brookside’s Motor Manufacturing plant production function is y ( K, L ) = 25 √ KL . The company is investigating a new outboard motor manufacturing technique. The management believes that if they adopts the new technique, the company’s production function for outboard motors will become: y ( K, L ) = 36 √ KL . Given that the company uses 4 units of machine hours, sketch his production function with the old technique and the new technique as he increases labor hours (a graph with output as y-axis and labour hour as x-axis). With the new technique, do labor hours contribute more to production? Econ 2000 Problem Set 4 2 / 2

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