Economic Applications

14J5. The rate of net investment is / - 40r1* and capital stock at I « 0 is 75. Find the capital function A'.

14.26. The rate of net investment is / - 6Or1", and capital stock at / • I is 85. Find K.

1*27. Marginal cost is given by MC - (fTGdQ - 25 + 30(? - 9(?J. Fixed cost is 55. Find the (a) total cost, (b) average cost, and (c) variable cost functions.

a) TC = J MCdQ~ j (25 + 300 - 9Qs)dQ = 25(? * 15C2 - 3Ö5 + *

With FC - 55. at Q -0,TC - FC - 55. Thus,c- FC-55 and TC - 2SQ + \5Q> - 3<?%+55.

14M. Given MC - JTC/dQ -32+18Q- 12Q\ FC - 43. Find the (a) TC, (ft) AC and (c) VC functions.

А) TC • J MCifC> - J (32 + 1RG - 12QVG - 32Q - 90* - 4C?3 ♦ c

б) AC-—-32 +90-40* + ^ c) VC = TC - FC - 32C? + 9Q1 - 4Q>

14.29. Marginal revenue is given by MR = dlRJdQ = 60 - 2Q - 2Q-\ Find (a) the TR function and (b) the demand function P - /((>).

At Q « 0. TR - 0. Therefore c = 0. Thin, TR = 60(?

TR = PQ. Therefore. P = 1R/Q. which is the same as saying that the demand function and the average revenue function axe identical. Thus. P = AR = TR/<? = 60 - Q - ]Q*.

14J0, Find («) the total revenue function and (b) the demand function, given

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