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Consider a rm with a production function given by F(L, K): A (L3+ K3) where A > 1 is a xed scaling factor that affects rm's productivity. That 1s, a higher A means that a rm 1s able to produce more output with a given combination of labour and capital. For now you can assume that A is constant. Let the wage paid to workers be 20 = 10 and the rental rate paid to capital owners be r = 100. (a) With L on the horizontal axis and K on the vertical axis, draw the rm's expansion path, which describes the combination of L and K that a rm will choose to minimize costs at each output level. Derive a formula for the path. You do not need to depict the output level, or the isoquants. b) Derive formulas for the rm's conditional labour L" (g) and capital K *(q) input demands as a flmction of q. If a rm improves its productivity and reaches a higher level of A, how does this affect the conditional demand for labour and capital respectively? (c) Derive an expression for this rm's average cost of production in terms of q and A. (d)_ If the rm' 5 level of production has an average cost (in dollars) of AC: 3, how much additional output would the rm get from a small mcrease in capital expenditure, per dollar? What about from a small increase in labour expenditure, per dollar? Please show your work