Throughout history from 19th century grain elevators that we just discussed to the British goldsmiths of the 17th century, warehousing and banking have been intimately related. To understand this relationship, I now ask you to develop a formal model. There are 3 dates and 3 types of agents (the farmer, the laborer, and the warehouse). At date 0, the farmer has an endowment e of twelve units of grain and can borrow B units from the warehouse at a gross interest rate of one. The farmer can use his endowment and any loan from the warehouse to make an investment i = B + e in production. The farmer's production technology transforms labor eort from the laborer l and this investment at date 0 into y units of grain at date 1: y = 4min{i,l}. The farmer can then make a decision to repay his loan and deposit whatever is left yB at the warehouse or not repay the loan and store his grain privately. If the farmer stores his grain privately, it depreciates at rate = 20% while if he stores it in a warehouse, it does not depreciate. The laborer, after receiving his wages wl, deposits them in the warehouse. Finally at date 2, the farmer and labor consume. Assume that the rate the warehouse charges on deposits as well as the wage paid to the laborer w are equal to one.

1. Calculate the consumption for the farmer and laborer where there is warehousing but the warehouse can lend the farmer B units at date 0 by issuing "fake receipts." Hint: Calculate output as a function of the loan size B. Then calculate the largest loan size that the farmer can credibly commit to paying back meaning the farmer prefers to pay back the loan rather than store his goods privately: yB (10.2)y.Also, use the farmer's budget constraint i + wl = 12 along with the fact that the farmer wants to set i = l to determine ouput.