MICROECONOMIC MODELING: SUPPLY AND DEMAND

    1. Suppose that the market for fine champagne is presently at a free-market equilibrium quantity of 8 and price of $16. Two researchers agree that the supply curve has the following equation:
            Qs = 1/2·P
but they disagree about the demand for champagne:
            Researcher 1: Qd = 16 - 1/2·P
            Researcher 2: Qd = 12 - 1/4·P
    a. Contrast these two equilibrium situations in two supply and demand diagrams. Which demand curve appears to be less price-elastic? Explain briefly how you decided.
    b. Suppose that the government is considering a tax of $12 per bottle of champagne.
    c. Contrast the forecasts of the two researchers about the impact of the wine by calculating each of the following:

    2. Consider the following information about the market for books:
            Qd = 16 - 2·P_B
            Qs = 1 + P_S
    a. Calculate the initial free-market equilibrium, and depict it in a supply and demand diagram.
    b. Now suppose the government legislates a $3 per book subsidy. Calculate each of the following:

    3. Answer the following questions about the online news article, "Gasoline dealers absorbing part of nickel tax."
        a. Use information approximating the values reported in Passage A and Passage B to draw a supply and demand diagram for the gasoline market in which you show (1) an initial equilibrium (before the tax went into effect) and (2) a final equilibrium (after the tax went into effect).
        b. Clearly label in your diagram the new price paid by buyers (including the tax) and the new (after-tax) price received by gasoline sellers (round your price values to the nearest penny). Is the price information you labeled in your diagram consistent with the title of the article? Explain briefly.
        c. Indicate each of the following consequences of the tax in your diagram:
            (1) the change in consumer surplus
            (2) the change in producer surplus
            (3) the government tax revenues collected
            iv. the welfare loss resulting from the tax.
        d. The demand for most products, including gasoline, tends to be more elastic in the long run than in the short run, since the long run gives consumers more time to find substitutes. Considering that information, decide whether each of the following is true or false, and explain briefly:
            (1) The revenue that government collects from a tax on a product tends to be larger in the long run than in the short run.
            (2) The amount of underprodution and therefore the welfare loss from a tax on a product tends to be larger in the long run than in the short run.

MACROECONOMIC MODEL BUILDING: THE KEYNESIAN CROSS

    4. Consider the following macroeconomic model of the economy (the "A" subscripts denote autonomous spending):
            C = C_A + MPC·DY = 40 + .8DY
            I = I_A = 75
            G = G_A = 125
            X-M = (X-M)_A = 0
            T = T_o = 0
    a. Calculate the equilibrium level of income and the size of the spending multiplier (m).
    b. In a Keynesian cross diagram, draw the 45^o-line representing AE=Y, and also draw the equation for AE.
    c. Label the equilibrium point in your diagram for part b.
    d. Calculate the equilibrium levels of consumption and savings.
    Now suppose that government spending rises by 50.
    e. Calculate the change in equilibrium aggregate expenditure and the new equilibrium level of aggregate expenditure.
    f. Depict the new equilibrium in your diagram.

    5. Consider the same model as for the previous problem (with government spending back at its original level of 125). But now suppose that there is the following level of lump-sum taxes:
            T = T_A = 50
    a. Calculate the equilibrium level of aggregate expenditure.
    b. Calculate the equilibrium levels of disposable income, consumption and savings.
    c. Calculate the size of the spending multiplier.

    6. Consider the same model as for problem 4, but now suppose that taxes consist of income taxes as follows:
            T = tY = .25*Y
    a. Calculate the equilibrium level of aggregate expenditure.
    b. Plot your equilibrium in a Keynesian cross diagram.
    c. Calculate the equilibrium levels of taxes, disposable income, consumption and savings.
    Now suppose that government spending rises by 50.
    d. Calculate the change in equilibrium aggregate expenditure and the new equilibrium level of aggregate expenditure.
    e. Depict the new equilibrium in your diagram.
    f. Compare the size of the government spending multiplier and the change in equilibrium aggregate expenditure in this case with the corresponding values from problem 4. Briefly explain the economic reasoning behind the differences you observe.

    7. Consider again the same model as for problem 4, with no taxes, but with the following equation for net exports:
            X-M = NX_A - MPM*Y = 60 - .05*Y
where MPM = the economy's marginal propensity to import.
    a. Calculate the equilibrium level of aggregate expenditure.
    b. In a Keynesian cross diagram, draw the 45^o-line representing AE=Y, and plot the equation for AE.
    c. Calculate the equilibrium levels of consumption, savings, and net exports.
    Now suppose that government spending rises by 50.
    d. Calculate the change in equilibrium aggregate expenditure and the new equilibrium level of aggregate expenditure.
    e. Depict the new equilibrium in your diagram.
    f. Calculate the new equilibrium levels of consumption, savings, and net exports.
    g. Compare the size of the government spending multiplier and the change in equilibrium aggregate expenditure in this case with the corresponding values from problem 4. Briefly explain the economic reasoning behind the differences you observe.