The practice of charging interest on money that is lent by one party to another, while commonplace now, has been historically controversial. Major religions
have prohibited the charging of interest in the past (and some do so today), and governments have often codified this moral objection to interest in what is known as usury laws that limit the amount of interest that individuals can charge one another.
A. Usury laws are thus simply an example of a price ceiling in the market for financial capital.
(a) Illustrate a demand and upward sloping supply curve in the market for financial capital (with the interest rate on the vertical axis). Denote the equilibrium interest rate in the absence of distortions as r∗.
(b) If usury laws prohibit interest rates above r∗, will they have any impact?
(c) Suppose the highest legal interest rate r̅ is set below r∗. Explain what will happen to the amount of financial capital provided by suppliers of such capital.
(d) In light of the fact that financial capital is essential for an economy to grow, what would you predict will happen to economic growth as a result of such a usury law?
(e) How is the decrease in financial capital from usury laws related to the interest rate elasticity of demand? How is it related to the interest rate elasticity of supply?
(f) Consider how a new equilibrium is likely to be reached in the financial market after the imposition of such a usury law. In addition to the dampening effect of less capital on economic growth, can you think of another related factor that may dampen such growth?
(g) How is this factor (relating to the effort expended on securing financial capital) affected by the interest rate elasticity of demand and supply?
B: Suppose that demand and supply curves are similar to those used in exercise 18.7, with demand given by kD = (A/r )α and supply by kS = (Bw)β.
(a) Derive the interest rate elasticity of capital demand and supply.
(b)What is the equilibrium interest rate in the absence of price distortions?
(c) What is the equilibrium level of financial capital transacted in the absence of any price distortions?
(d) Suppose A = 24,500, B = 500 and α = β = 1. Determine the equilibrium interest rate r∗ and the equilibrium level of financial capital k∗.
(e) Suppose the usury law sets a maximum interest rate r̅ = 5. What is the new level of financial capital k′ transacted—and how big is the drop (k∗−k′) in financial capital as a result of the usury law?
(f) If the new equilibrium is reached by investors expending additional effort to get to financial capital, what is the equilibrium effort cost c∗?
(g) Create a table with r ∗, k∗, k′, (k∗ −k′) and c∗ at the top. Then fill in the first row for the case you just calculated—i.e. A = 24,500, B = 500 and α = β= 1.
(h) Next consider the case where A = 11,668, B = 500, α = 1.1 and β = 1. Fill in the second row of the table for this case—and explain what is happening in terms of the change in interest rate elasticities.
(i) Finally, consider the case where A = 24,500, B = 238.1, α = 1 and β = 1.1. Fill in the third row of the table for this case — and again explain what is happening in terms of the change in interest rate elasticities.