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1. Imagine a firm has the following short-run production function: Q=f(L,K)=KLL2 Assume K=250. a. Derive expressions for marginal product of labor (MPL) and average product of labor (APL). b. Use Excel to compute and graph the following: output (that is, the short-run production function itself), MPL. and APL for L=0,,100. [Note: For submission, please copy/paste your graphs from Excel into Word and be sure to label each graph. Also, you do not need to copy/paste the data itself (only the graphs).] 2. For the following Cobb-Douglass production function, Q=f(L,K)=L0.7K0.8 where Q is measured in 1000 s of units of output per week, L is measured in hundreds of worker hours per week, and K is measured in 1000 's of machine hours per week: a. Derive expressions for marginal product of labor (MPL) and marginal product of capital (MPK). b. Derive the expression for marginal rate of technical substitution, MRTS. c. Does this production function display constant, increasing, or decreasing returns to scale? Prove your answer mathematically. d. Assume the wage paid to labor is W=$7 and the rental rate of capital is R=$256. If the firm needs to produce Q=4 (thousand) units of output per week, solve for its cost-minimizing combination of capital and labor inputs. e. Based on your answer in part (d), what is the firm's total cost of producing Q=4 (thousand) units of output? 3. In the short-run, a perfectly competitive firm has a fixed cost of $1000 per month. Its marginal cost curve is MC(Q)=20Q+100 where Q is units of output per month. a. What is the firm's short-run total cost (TC) function? b. What is the firm's short-run average total cost (ATC) function? c. What is the firm's short-run shutdown price? d. Use Excel to compute and graph the following: MC,ATC, and AVC for Q=0,,100, One bonus point will be awarded for combining all three curves on the same graph. [Note: For submission, please copy/paste your graph(s) from Excel into Word and be sure to label each curve. Also, you do not need to copy/paste the data itself (only the graphs).] Now, assume the market equilibrium price is $500. e. What is the firm's profit-maximizing quantity? f. Based on your answer from part (d), compute the firm's profit (or loss) per month. g. Based on your answer from part (e), if all firms (and potential entrants) in this market are identical, what would we expect to happen in the market over the long-run