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Consider the demand and supply equation for one-year discount bonds

September 28, 2022

Consider the demand and supply equation for one-year discount bonds with a face value of $990:
Demand: Price = -0.5 * Quantity + 1200
Supply: Price = Quantity + 300
What is the equilibrium price and quantity in this bond market? What is the implied interest rate on the one-year discount bond?
Suppose a foreign government buys 100 bonds from this bond market. Derive the new bond demand equation after the foreign government’s bond purchase. Assume the bond supply equation does not change. What is the new equilibrium price, equilibrium quantity, and implied interest rate in this bond market? (for price and quantity, keep one decimal place; for interest rate, keep three decimal places if your write your result in general number format or keep one decimal place if your write your result in percentage format)
In 2021, the US stock market’s average dividend-price ratio was 1.4%, the investors expected that the average dividends would grow by 4% a year in the future, and the 10-year treasury bond yield (risk-free interest rate) was 1.5%. What was the implied risk premium on the US stocks in 2021?
Suppose at the end of 2022, investors find that the US stock market’s average dividend-price ratio rises to 2% and the 10-year treasury bond yield rises to 3%; analysts find that the risk premium on the US stocks rises to 5% and expect the future inflation rate will be 4.5%. Given the information and assume that the investors expect the US stock dividends will grow at the same rate as nominal GDP in the future, what real GDP growth rate should the investors expect the US economy to have?
Suppose the US economy experiences a recession in 2023. However, the Federal Reserve decides to hold the money supply constant. Draw a graph for the bond market to illustrate the effect of economic recession on the bond market. In your graph, label both axes and all curves, and indicate clearly how the equilibrium price and quantity should change. Explain the reasoning behind the movement of bond demand and supply and the change in equilibrium price and quantity in your graph. Make sure you use all information provided above. (You can either draw the graph using word drawing tools or draw it by hand and then take a picture)

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