6. The cost function c(wl, w2, y) expresses the cost per unit of output of produ

Question

6. The cost function c(wl, w2, y) expresses the cost per unit of output of producing y units of output if equal amounts of both factors are used. ANS: F DIF: 2 7. A competitive, cost-minimizing firm has the production functionf(a. y)-x+2y and uses positive amounts of both inputs. If the price of x doubles and the price of y triples, then the cost of production will more than double ANS: F DIF 2 8. The total cost function c(wl, w2, y) expresses the cost per unit of output as a function of input prices and output ANS: F DIF: 3 9. A firm uses a single variable input x to produce outputs according to the production function f(r)- 300x+62 This firm has fixed costs of $400. This firm's short-run marginal cost curve lies below its short-run Oerage variable cost curve for all positive values ofx ANS: F DIF: 3

Explanation / Answer

6) Cost function shows the total output produced with a given combination of inputs which can be equal or unequal to each other. For example, labor is priced at w1 and capital is priced at w2. This gives cost function as C = w1L + w2K where L = K , L < K, L > K, all possibilities are equally likely

7) Currently firm is using both inputs which, given that production function is downward sloping straight line, shows perfect substitution between inputs. Hence the firm must be following the rule

MPx/Px = MPy/Py

or MPx/MPy = Px/Py

Now see that MPx is 1 and MPy is 2 so we have MRTS = 1/2. Hence originally, Px/Py should be 1/2

If Px doubles and Py triples, we have price ratio = 1*2/2*3 = 1/3

Since now MRTS is 1/2 and price ratio is 1/3, we have MRTS > Price ratio and firm will use only x input and no y input. Then, the cost of production is doubled because price of x is doubled.

8) Total cost function expresses the total cost as a function of output only. The reason why input prices are written is that sometimes, input prices are taken within the cost function when their exact values are not given

9) With given function, MC = 300 + 12x and AVC = 300 + 6x. Now for all x> 0, MC is higher than AVC. Hence MC lies above AVC

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