Suppose that the quantity of corn supplied depends on the price of corn (P) and the amount of rainfall (R). The demand for corn depends on the price of corn and the level of disposable income (I). The equations describing the supply and demand relationships are Qs = 20R + 100P and Qd = 4000 − 100P + 10I.
Sketch a graph that shows the effect of an increase in rainfall on the equilibrium price and quantity of corn. (2 marks)
Sketch a graph of demand and supply curves that shows the effect of a decrease in disposable income on the equilibrium price and quantity of corn. (2 marks)
The demand for beer in Japan is given by the following equation: Qd = 700 − 2P − PN + 0.1I, where P is the price of beer, PN is the price of nuts, and I is average consumer income.
What happens to the demand for beer when the price of nuts goes up? Are beer and nuts substitutes or complements? - prove (2 marks)
What happens to the demand for beer when average consumer’s income rises? (1 marks)
Graph the demand curve for beer when PN = 100 and I = 10,000. (2 marks)
Justin has the utility function U = xy, with the marginal utilities MUx = y and MUy = x. The price of x is $2, the price of y is py, and his income is 40. When he maximizes utility subject to his budget constraint, he purchases 5 units of y.
What must be the price of y and the amount of x consumed? (1 marks).
Prove that this allocation follows the equi-marginal principle (2 marks).
What would be the new bundles of x, y if Px was $3 (2 marks).
Terry’s utility function over leisure (L) and other goods (Y ) is U(L, Y ) = Y + LY. The associated marginal utilities are MUY = 1 + L and MUL = Y. He purchases other goods at a price of $1, out of the income he earns from working. Show that, no matter what Terry’s wage rate, the optimal number of hours of leisure that he consumes is always the same.
What is the number of hours he would like to have for leisure? (1 marks)
Determine the MRS of leisure for labour (2 marks)
Draw a leisure-influenced labor curve (2 marks)
What is the marginal product of labour and capital (1 marks)
What is the marginal rate of technical substitution of labor for capital (2 marks)
What is the elasticity of substitution at a point K = 1, L = 1 if we increase K by one unit? (2 marks)
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