Problem 1: Given the following total revenue (TR) and total cost (TC) functions, find the quantity of output (Q) that would maximize profit (π). Note that profit function is: π = TR - TC. TR = 1400Q - 7.5Q2 TC = Q3 - 6Q2 + 140Q + 750
Problem 2: Prove that marginal cost (MC) must equal marginal revenue (MR) at the profitmaiming level of output. Note: TC dQ d MC and TR dQ d MR . Hint: π = TR - TC.
Problem 3: Find the marginal cost (MC) for the following average cost function (AVC): AVC = 1.5Q + 4 + 46/Q. Hint: TC=AVC*Q.
Problem 4: An isoquant depicts different combinations of inputs K (Capital) and L (Labor) that can be used to produce a specific level of output Q. One such isoquant for the output level Q = 2,144 is 2144 = 16 K1/4 L3/4 Using implicit differentiation find the slope of the isoquant dK/dL which is called Marginal Rate of Technical Substitution (MRTS) and evaluate MRTS at K = 256 and L = 108.
Problem 5: A firm producing two good x and y has the profit function: π =64x - 2x2 + 4xy - 4y2 + 32y - 14 Find the profit-maximizing level of output for each of the two goods (x and y).
Problem 6: Given a three-sector income determination model in which Y = C + I0 + G0 T = T0 + t*Y C = C0 + b*YdYd = Y - T Where: I0, G0, T0, C0 > 0 and 0 < b, t < 1
Determine the magnitude and direction of a 1-unit change in government expenditure (G0), lump-sum taxation (T0), and the tax rate (t) on the equilibrium level of income (Y).
Problem 7: Given Q = 700 - 2P + 0.02Y, where P=25 and Y = 5000. Find the price elasticity of demand (dQ/dP) and the income elasticity of demand (dQ/dY).
Problem 8: Given Q = 10 K0.4 L0.6, find the marginal productivity of capital (dQ/dK)and marginal productivity of labor (dQ/dL) and determine the effect of on output of an additional unit of both capital and labor at K = 8, L= 20.
Problem 9: Using the following table, calculate the average annual growth rate of real GDP for US and India between 1990 and 2010. Assume similar growth rates are forecasted for the foreseeable future for both US and India. Will India's economy ever be larger than that of the US? If yes, estimate the year at which India's GDP will overtake that of the US. Real GDP (2005 Billion $) 1990 2010 India 350.24 1,246.91 United States 8,228.92 13,595.64