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Consider a rm with a production function given by F (L, K ) = A (L2 +K2) where A 2 1 is a xed scaling factor that affects rm's productivity. That is, a higher A means that a rm is 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 m = 30 and the rental rate paid to capital owners be r = 100. (a) [3/ 15 r 3 marks] 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) [5/15 nar 3.33 marks] Derive formulas for the rm's conditional labour L" (q) and capital K *(q) input demands as a function 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? ((3) [3/ 15 wr 3 marks] Derive an expression for this rm's average cost of production in terms of q and A. (d) [4/ 15 Mr 2.67 marks] If the rm's level of production has an average cost (in dollars) of AC 2 2, how much additional output would the rm get from a small increase in capital expenditure, per dollar? What about from a small increase in labour expenditure, per dollar? Please show your work