Suppose the production function in medieval Europe is Y= K0.5L0.5, where K is the amount of the land and L is the amount of labor. The economy begins with 100 units of land and 100 units of labor.Production function: Y= K0.5L0.5K = Land = 100 units.L= Labor = 100 units.•How much output does the economy produce?Y= K0.5L0.5Y = 100^0.5 * 100^0.5Y = 100The output of the economy is 100 units.•What are wage and rental price of the land?ΔProfit = ΔRevenue − ΔCost = (P * MPL) − W.P = Price level.MPL = Marginal price of labor.W = WageBut in the perfectly competitive scenario, ΔProfit = 0 for all the firms.So,W = P*MPLAs P is not given, we will assume that the price level P =1Real wage = W/P = MPL = dY/dL = …show more content… So MPL = Real Wage = 0.5.Similarly,Rental price of land = MPK = dY/dK = d(K0.5L0.5)/dK = 0.5* L0.5/K0.5 Here K = L = 100 units.So MPK = Rental price of land = 0.5.•What share of output does labor receive?Cobb–Douglas production function.F(K, L) = A (K)^a * (L)^(1-a) a: constant between zero and one that measures capital’s share of income. That is a determines what share of income goes to capital and what share goes to labor.A: Parameter was greater than zero that measures the productivity of the available technology.Converting the given function Y= K0.5L0.5 into the above form.We get a = 0.5 and A =1.Thus, 50% share of output does labor receive.•If a plague kills half of the population, what is the new level of Output.L’ = L/2 = 100/ 2 = 50Y= K0.5L’0.5Y = 100^0.5 * 50^0.5Y = 70.71 unitsThe output of the economy is 70.71 …show more content… That is a determines what share of income goes to capital and what share goes to labor.A: Parameter was greater than zero that measures the productivity of the available technology.a = 0.3So, 30% output will go to land, and 70% of output will go to the labor.L’ = 1.1LY= K0.3L0.7Y’ = K0.3L’0.7 = K0.3 * 1.1 L 0.7 = 1.1 K0.3L0.7 = 1.1YSo, output increases by 10%.Rental price of capitalMPK = d(Y)/ dK = d(K0.3L0.7)/dK = 0.3 L0.7/ K0.7MPK’ = 0.3 L’0.7/ K0.7 = (0.3*1.1) L0.7/ K0.7MPK’ = 1.1MPKThe rental price of capital will increase by 10%.Real wage = MPLMPL = d(Y)/ dL = d(K0.3L0.7)/dL = 0.7 K0.3/ L0.3MPL’ = d(Y)/ dL’ = d(K0.3L0.7)/dL’ = 0.7 K0.3/ (L0.3*1.1) = MPL/1.1MPL’ = 0.91 MPLThe real wage decreased by 9%.K’ = 1.1KY= K0.3L0.7Y’ = K’0.3L0.7 = 1.1* K0.3L0.7 = 1.1YSo, output increases by 10%.Rental price of capitalMPK = d(Y)/ dK = d(K0.3L0.7)/dK = 0.3 L0.7/ K0.7MPK’ = 0.3 L0.7/ K’0.7 = 0.3 L0.7/ K0.7 *1.1 = MPK / 1.1MPK’ = 0.91MPKThe rental price of capital will decrease by 9%.Real wage = MPLMPL = d(Y)/ dL = d(K0.3L0.7)/dL = 0.7 K0.3/ L0.3MPL’ = 0.7 K0.3/ L’0.3= (0.7 * 1.1) K0.3/ (L’0.3) = MPL*1.1MPL’ = 1.1 MPLThe real wage will increase by