ECON HW #4

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Feb 20, 2024

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Ilana Berger, Jessica Gonsalves, Sankalp Khare, James Lee, Cesar Valiente Professor Kirsten Daniel Microeconomics for Management Group Homework # 4 Problem # 1 Standard Enterprises produces an output that it sells in a highly competitive market at a price of $100 per unit. Its inputs include two machines (which cost the firm $50 each) and workers, who can be hired on an as-needed basis in a labor market at a cost of $2,800 per worker. The relevant production data are summarized in the table below. a) Based on these production data, calculate the marginal product of labor, the average product of labor, as well as the value of marginal productivity of labor. Extend the table to add those columns. P = 100 MP L = ΔQ , VMP L = P x MP L AP L = Q/L K L Q MP L AP L VMP L 2 0 0 2 1 60 60 60 6000 2 2 100 40 50 4000

2 3 129 29 43 2900 2 4 148 19 37 1900 2 5 160 12 32 1200 2 6 168 8 28 800 b) How many workers should the firm employ to maximize its profits? For maximum profit, VMP L >= W => when VMP L >= 2800 => 3 workers should be employed to maximize profits. Problem # 2 Crew Brew produces a popular brand of beer in its mini-brewery located on a small river in Wisconsin. It uses a special formula, combined with the fresh water from the local stream, to produce a drink popular with local folks and tourists who visit during the summer fishing season, and autumn deer hunting season. The production function of Crew follows the formula: Q=50(K+L) Where Q = Barrels of beer, K = units of capital, and L = units of labor. a) Suppose that capital can be purchased for $8 per unit, and labor costs $6 per unit. What is the optimal combination of inputs for the firm to employ? MP K / K = 6.25 MP L / L = 8.33 => Since, MP K / K is less than MP L / L ,the Crew firm should focus on labor to maximize profit. b) Suppose that the cost of inputs changes to $7 for a unit of capital, and $9 for a unit of labor. What is the new optimal combination of inputs? MP K / K = 7.14 MP L / L = 5.55

Now since MP K / K is greater than the MP L / L the firm should focus on getting more capital to increase profit. c) Explain the results of a) and b). MP K = 50 , MP L = 50 Since, MP K = MP L => Labor and Capital are perfect substitutes. Problem # 3 The firm ́s production function is: 𝑄 =5 ? −0.5 ? ² and ?𝐶? =18 MR = 6 a) Assuming that the firm is operating in the short run, with fixed capital, what is the optimal amount of labor (L) that should be hired? MP L = 5 - L MRP L = MP L x MR = 6 x ( 5 - L ) = 30 - 6L For optimal amount of labor, MRP L = MC L => 30 - 6L = 18 => L = 2 2 laborers should be hired. b) What is the firm ́s operating profit? Operating profit = MR x Q - (MC L x L) = 6(5L - 0.5 L 2 ) - (18 x L) = 6(5x2 - 0.5x2 2 ) - (18 x 2) = 12 => Operating profit is 12

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Problem # 4 The production manager of a clothing manufacturer estimates that the total annual cost of producing suits is given by the equation 𝐶 =5000+4100 𝑄 −8 𝑄 ²+0.004 𝑄 ³ a) If the market price of suits is constant, what is the shutdown level of output? AVC = VC / Q VC = 4100Q - 8Q^2 + 0.004Q^3 => AVC = ( 4100Q - 8Q^2 + 0.004Q^3) / Q = 4100 - 8Q + 0.004Q^2 => ∂ AVC/ ∂ Q = -8 + 0.008Q For shutdown, -8 + 0.008Q = 0 => Q = 1000 b) What is the minimum price the firm can accept? Mini Price = minimum of AVC AVC at Q = 1000 , is 4100 - 8 * (1000)^2 + 0.004 * (1000)^3 AVC = 100 => Price is $100 Problem # 5 Kevin Coughlin, a lawyer working for a large law firm and earning $70.000 per year is contemplating setting up his own law practice. He estimates that renting an office would cost $12.000 per year, hiring a legal secretary would cost $45.000 per year, and purchasing the required supplies, paying for electricity, telephone, and so forth would cost another $6.000. The lawyer estimates that his total revenues for the year would be $100.000, and he is indifferent between keeping his present occupation with the large law firm and opening his own law office. a) How much would be the explicit costs of the lawyer for running his own law office for the year?

Explicit costs = Rent of office+ salary of legal secretary+ rent for office equipment + cost of essential supplies = $12000 + $45000 + $6000 = $63000 => Explicit costs = $63000 b) How much would the accounting costs be? The implicit costs? The economic costs? Implicit costs = $70,000 Economic costs = Implicit + Explicit costs => Economic costs = $63,000 + $70,000 = $133,000 c) Should the lawyer go ahead and start his own practice? Profit = 100,000 - 133,000 = -33,000 => The Lawyer should not start the business as it will be at a loss.

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