Consider the U.S. economy where checks are still widely used. Suppose that there exist only two payment media: currency notes (the legal tender) and checks. Each merchant accepting a check is subjected to a fixed pertransaction cost of τM,ck which reflects the value of time spent on reading the information on the check and going to the bank in order to deposit the check. Each merchant accepting currency notes and coins is subjected to the cost summarized by equation (8.14). Each buyer who writes a check is subjected to a fixed cost of τ B,ck associated with the time it takes to write a check. Each buyer who pays withcurrency notes and coins is subjected to the cost summarized by equation (8.15). Assuming that τM,ck > τM, and that τ B,ck > τ B, answer the following questions:

(a) Which type of payment medium minimizes merchants’ transaction cost at every transaction’s value of p, p > 0. Plot your result on a graphsimilar to Figure 8.5.

(b) Which type of payment medium minimizes buyers’ transaction cost at every transaction’s value of p, p > 0. Plot your result on a graphsimilar to Figure 8.6.

(c) Find the equilibrium usage of payment media for every transaction value p, p > 0, and plot your result on a graphsimilar to Figure 8.7. Hint: There can be two cases depending on the parameters of the model.

(d) Suppose that for every transaction value p there is one buyer and one seller. For every transaction value p, determine which payment media minimizes social cost. Hint: Social cost is defined as the sum of the buyer’s and merchant’s transaction costs.

(e) Conclude whether checks are over-used or under-used in this economy. Explain your result.