Econ 308 1st Edition Exam # 2 Study Guide1. A firm’s short run production function is given by Q=1/2L2 for 0 ≤ L ≤ 2and Q=3L-1/4L2 for 2 < L ≤ 7a. Sketch the production function.b. Find the maximum attainable production. How much labor is used at that level?c. Identify the ranges of L utilization over which the marginal product of labor is increasing and decreasingd. Identify the range over which the marginal product of labor is negative.Q=3L-1/4L^2 MPL=3-1/2L=0 L=6 2. A daily production function for calculators is Q = 12L2- L3. Show all your work for the following questions. a) What is the marginal product equation for labor?b) What is the APL function? Q=12L^2-L^3 APL= Q/L = 2L-L^23. Sketch graph a standard short-run production function, and identify on it the points wherethe average product peaks, the marginal product peaks, and the marginal product reaches zero, and the average and marginal product intersect. APL is maximized4. In the production function Q = 10L1/2K1/2calculate the marginal product equations of both inputs. Alpha= ½ Beta=1/2K*LQ=10K^1/2L^1/2= 5k^-1/2L1/2MPL=5k^1/2L^-1/25. In the production function Q = 10L1/2K1/2 calculate the slope of the isoquant when the entrepreneur is producing efficiently with 9 laborers and 16 units of capital. (Hint: The slope of the isoquant = the ratio of the marginal product of labor to the marginal product of capital.) MPL/MPK> MRTS6. In the production function Q = 10L1/2K1/2if the inputs are quadrupled, are there economiesof scale? In the production function Q = 10L1/2K1/2is diminishing returns a characteristic of this production function?Alpha=Beta=1/2---CRTS DRTS/law of diminishing return- short run- Q only function of L1. A firm has access to two production processes with the following marginal cost curves:MC1 = 0.4Q and MC2 = 2+0.2Qa. If it wants to produce 8 units of output, how much should it produce with eachprocess?b. If it wants to produce 4 units of output?Q1+Q2=8.4Q=2+0.2Q2 Q=6 Q2=2Q1+Q2=4 .4Q1=2+0.2Q2 Q1=4 Q2=0 2. Alex has a total cost function give by TC (Q) = Q2-10Qa. What is Alex’s average cost function?Q-10c. What is Alex’s marginal cost function?2Q-10c. Calculate Alex’s total cost, average cost and marginal cost for Q = 20, 30 and 40?3. Freddie has a production function given by Q = F(K,L) = 3K1/ 2L1 /2, in the short runcapital is fixed at K=100.The wage rate is w=$9 and the rental rate for capital is $5.a. What is Freddie’s short run production function?Q=3(100)^1/2=30L^1/2b. Calculate Freddie’s short run total cost function where STC = r*K+w*L.STC=rk*Wl5(100)+9L= 500 +9L500+9(Q^2/900)STC=500 +(Q^2/100)c. What is Freddie’s short run average cost function?500/Q+Q/1004. A firm produces output with the production function: Q = F(K,L) = K1/ 2L1 /2Where K and L denote its capital and labor inputs, respectively. If the price of labor is 1and the price of capital is 4, what quantities of capital and labor should it employ if itsgoal is to produce 2 units of output? MPL= 2Q/2L=1/2k^1/2L^1/2MPK=1/2L^1/2K^-1/2 L=4k K/L=1/41. In a competitive industry consisting of 10,000 firms, the short-run marginal cost curvefor each firm is given by MC = 200 + 30 Q. The demand curve faced by the industry isgiven as P = 400 - .002 Q.a. Find the equilibrium price and quantities for the industry and each firm.b. Find the producer and cosnumer surpluese for the industry at the equilibrium price.c. Find the elasticity of supply.N=10,000 MC=200 +30Q perfectly competititveMR=MC p=200+30Q--- Qi+ (p-200)1/30Market supply curve- 10000/30(p-200)=QP*=320Q*=40,000PS=1/2(40,000)(320-200)CS=1/2(40,000)(400-320)2. A firm in a competitive industry has a total cost function of TC = 0.2Q2-5Q + 30,whose corresponding marginal cost curve is MC = 0.4 Q – 5. If the firm faces a price of6.a. What quantity should it well? b. What profit does the firm make at this price?c. Shour the firm shut down?6=0.4Q-5Q=27.6- output levelTR=P*Q =6*27.5TR-TC=Pi= ^*27.5-.2(27.5)^2-5(27.5)+30 =121.25 firm shouldn’t shut down,positive3. Suppose a representative firm in a perfectly competitive, constant cost industry has acost function: TC = 4Q2+ 100 Q + 100.a. What is the long-run equilibrium price for this industry?b. If market demand if given by function Q = 1000 – P, where P denotes prices, howmany firms will operate in this long run equilibrium?LAC=4Q+100+100/QTC=4Q^2+100Q+100AC=TC/Q=4Q+100+100/Q4-100Q^2=0 Q=5 Q=1000-p p=140 Q=860 860/5=1724. The demand curve for a monopolist is given by P = 350 – 7 Q, and the short run totalcost curve is given by TC = 500 + 70 Q.a. What is profit-maximizing price and quantity?b. Find the monopolist’s economic profit.MR=350-14QTR=P*Q(350-7Q)Q=350Q-7Q^2 derivative= 350-14QTC=500+70Q MC=70MR=MC 350-14Q=70Q*=20P*=210210*20-500-70*20=23005. Suppose the monoplist has a demand curve given by P = 100 – Q, the total cost curvegiven by TC = 32 + Q2,a. What is the marginal cost curve?b. Find the monoplist’s profit-maximizing quantity and price.c. How much economic profit does the monoplist earn?D=100-QTC=32+Q^2MR=100-2Q100-2Q=@qQ*=25 p*=75 75*25-32-(25)^2=1218Q=f(k,l) in short run- labor inputlog run- K and L variable inputsTC= FC+VC FC does not vary with QMarginal cost= change in TC/Change in QMC> AC than AC increasesMC<AC AC decreasesC=Pk*K+PL* L- subject of