3) Marco has $100 worth of grain in period 1 but gets no grain in period 2. Marco has two choices. He can store the grain that he does not consume in period 1. This results in a loss of 20% of the grain due to pests. Assume that with this option he will choose to consume 68 units of grain in period 1 and 26 units in period 2. Instead, Marco can sell the grain he does not consume in period 1 and lend the money from that sale to someone today at an interest rate of 10%. He can then use the repayment of that loan to buy gain in period 2. a) Based on this information, draw a diagram that outlines Marco's choices. Is he definitely better off once the opportunity to lend is available to him? b) Relative to his initial equilibrium point, does he unambiguously consume more in both periods once he can lend out the excess he does not consume in period 1? c) Now assume that Marco can sell any excess grain he doesn't consume in period 1 and invest the money he gets in a new type of risky activity. There is a 50 per cent chance that it makes a return of 25 per cent on his investment in that activity, and a 50 per cent chance it makes zero return (but he will not lose the money he invested in the scheme). Give reasons why Marco would or would not undertake this investment (there is no need to draw a graph).

Assume a consumer has current-period income y = 200, future-period income y′ = 150, current and future taxes t = 40 and t′ = 50, respectively, and faces a market real interest rate of r = 0.05, or 5% per period. The consumer would like to consume according to the following utility function: U (c, c′ ) = ln(c) + ln(c′ ). Show mathematically the lifetime budget constraint for this consumer. Find the optimal consumption in the current and future periods and optimal saving. Suppose that instead of r = 0.05 the interest rate is r = 0.1. Repeat parts (a) and (b). Does the substitution effect or the income effect dominate?

The following table shows the quantity D of wheat, in billions of bushels, that wheat consumers are willing to purchase in a year at a price P, in dollars per bushel. D = quantity of wheat P = price 1.0 $2.05 1.5 $1.75 2.0 $1.45 2.5 $1.15 In economics, it is customary to plot D on the horizontal axis and P on the vertical axis, so we will think of D as a variable and of P as a function of D. (a) Show that these data can be modeled by a linear function. For each increase of 0.50 in D there is      of   in P. Find its formula. (Use P for price and D for quantity.)P =  −.6d+265      (b) Add the graph of the linear formula you found in part (a), which is called the market demand curve, to the following graph based on the following table for market supply curve. S = quantity of wheat P = price 1.0 $1.35 1.5 $2.40 2.0 $3.45 2.5 $4.50

Suppose your only source of income is work and that you are paid $20 per hour. This determines a budget constraint. You can buy free time at the expense of your income by working less. Likewise, you can get more income at the expense of your free time by working more. Suppose that you can choose how many hours you work. 5- Which of the two effects is the strongest in this example? How can you tell?