科目：個體經濟學 教授：鄭秀玲 試別：92學年度下學期第一次期中考 時間：2004年04月01日 ---------------------------------------------------------------------- 1.(10分) The prices of inputs (x1,x2,x3,x4) are (4,2,3,2), (1) If the production function is given by f(x1,x2)=min{x1,x2}, what is the minimum cost of producing one unit of output? (2) If the production function is given by f(x3,x4)=x3+x4, what is the minimum cost of producing one unit of output? 2.(15分) Firm A makes plastic product. Its production function is given by f(x1,x2)=(2x1+x2)^(1/2), where x1 is the amount of plastic used, x2 is the amount of wood used. (1) Does this production function exhibit increasing, decreasing, or constant returns to scale?(需以數學加以證明) (2) If firm A faces factor price (1,1), what is the cheapest way to produce 10 units of products? How much does this cost? (3) Please draw a set of isoquants for this firm. 3.(15分) A firm uses two inputs, labor(L) and capital(K) to produce its product. The wage rate for one unit of labor is $5, where one unit of capital costs $20 (1) Draw the isocost line for a $1000 expenditure by the firm on inputs. Draw a typical isoquant for an output level Q0 and depict(描述) the optimal input levels L and K. (2) Suppose the government institutes a minimum wage for labor of $6 per unit. In the short run, with capital fixed at K, show graphically how much it would cost the firm to hold its output constant at Q0. (3) Show the optimal factor mix the firm will use in the long run to produce Q0, given the minimum wage. 4.(8分) A firm has the following cost data: ------------------------------------------------ Output Total cost Variable cost ------------------------------------------------ 100 $7000 $4000 101 7400 4400 102 7900 4900 ------------------------------------------------ What are AVC, AFC, ATC and MC at these output levels? 5.(15分) Firm B's total cost function is C(y)=y^2+20 for y>0 and C(0)=0 (1) What is its marginal function? (2) What is its average cost function? (3) At what quantity is its marginal cost equal to its average cost? (4) At what quantity is its average cost minimized? (5) In a competitive market, what is the lowest price which he will supply a positive quantity in long-run equilibrium? How much would this firm supply at that price? 6.(15分) If output is produced according to Y=4LK, the price of K is $10, and the price of L is $5, then cost-minimizing combination of K and L capable of producing 8 units of output is_________. (請以數學加以證明並求解) 7.(7分) 在過去這二、三年來，全球經濟不景氣，台灣經濟亦然，有些廠商雖然已呈虧損 狀態，但仍持續經營，並未退出市場。請從生產成本的角度探討這類廠商的考量 為何？ 8.(15分)請繪圖說明如何從短期邊際成本(SMC)導出長期邊際成本。 (請以continuous level of plant size 的 case 來討論即可) --

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