In a particular country, there are two types of individuals: native (n) and foreigners (f). Each dedicate their 8 hours of labor to producing either luxury (x) and non-luxury goods (y). Native workers' utility function is given by Un = x04y0.6 whereas foreigners' is given by U, = x02y0.8. Both individuals do not care whether they produce x or y. The production function for each good is given by x = y = 5l, where l is the total labor devoted to the production of each good. 4l and Px a) What must be the price ratio, /py, be? Interpret your answer

Suppose farmers in a given market can either grow soy beans or corn on their land. In addition, suppose an increase in the demand for corn causes the price of corn to increase. All else equal, an increase in the price of corn creates an incentive for farmers to: Multiple Choice switch away from growing corn and into growing soy beans. switch away from growing soy beans and into growing corn grow less corn, but not change their production of soy beans. grow more corn, but not change their production of soy beans.

Problem 5: Consider an economy with production. The production functions for goods X and Y are given by: Y = = La Ly ဇာ where Lx +Ly = I. The utility function of the representative consumer is given by: U (x, y) = min {}} where all the parameters are positive. Determine the Walrasian equilibrium quantities of X and Y produced and sold in this economy.

Consider an economy where all production and all consumption is carried out by a single agent, Robinson Crusoe. Robinson, as a consumer, is endowed with H hours of time. His utility depends in hours of leisure, h, and coconuts, y: u(h, y) = (h)1−βyβ with 0 ≤ h ≤ H,β ∈ (0,1). Robinson, as a firm, can transform hours of labor, z, into coconuts y. His technology of production is given by y = f(z) = zα with α ∈ (0, 1). Let p denote the price of coconuts, w denote the price of leisure/labor, and π denote the firm’s profits. Note that the budget constraint of Robinson is py ≤ w(H − h) + π. Note that the budget constraint of Robinson is px ≤ w(H − h) + π, and that in equilibrium in the market of coconuts x = y and in the labor market h + z = H. Find the equilibrium allocation and price vector in equilibrium.