Suppose that the following equations refer to a simple national economy: C_t = 0

Question

Suppose that the following equations refer to a simple national economy: C_t = 0.375 Y_t - 1 I_t = 40 - 0.125(Q_t - 1 - Q_t - 2) where C_t = the consumption in year t Y_t = the income in year t Q_t = the production in year t I_t = the investment in year t Assuming that the usual equilibrium conditions hold, show that Y_t satisfies the difference equation Y_t - 0.25 Y_t - 1 - 0.125 Y_t - 2 = 40 It is given that Y_0 = 65 and Y_1 = 64.5, find the general expression for Y_t. Comment 011 the behaviour of this solution The price elasticity of demand for a commodity is given by. Create a differential equation that will assist in solving for the demand function. In a learning experiment, a subject is first given x minutes to examine a list of facts. The fact sheet is then taken away and the subject is allowed y minutes to prepare mentally for an examination based on the fact sheet. Suppose it is found that the score achieved by a particular subject is related to x and y by the formula Currently, students in the experiment have 10 minutes to examine the list of facts and 15 minutes to prepare mentally for the examination. Use marginal analysis to estimate the change in the score that will result if the invigilator decreases the time for examining the list of facts by one minute but increases the time for preparing for the examination by one minute. The Lorenz curve for a given country in the year 1997 may be approximated by Li(x) where The comparative curve for the same country in 1993 was approximated by L2(x) where Compute the Gini Indices for this country in 1993 and 1997. Interpret the difference in the indices. In the 2000-2001 academic year there were 430,164 Master's degrees granted by universities in the United States. Assume the future relationship between the number N of Master's degrees granted and the years t since 1999-2000 academic year is given by Use Implicit Differentiation or otherwise to find an expression for N'(t). The demand for a major domestic appliance is given by D_t = 50 + 25P_t where demand is given in hundreds of articles and price in dollars. The corresponding supply equation is given by S_t=-10 + 20P_t - 1. If the price is $143 when t = 0, What will the price be after three time periods have elapsed. Will there be an eventual convergence to some equilibrium price? if so, what will that price be?

Explanation / Answer

7a) As usual equilibrium conditions hold so Yt = Ct+It and Y=Q

Ct = 0.375Y(t-1)

It = 40-0.125(Y(t-1) - Y(t-2))

Yt = 0.375Y(t-1) + 40-0.125(Y(t-1) - Y(t-2)) = 40 + 0.25Y(t-1) + 0.125Y(t-2)

so Yt - 0.25Y(t-1) - 0.125Y(t-2) = 40

ii)

So from above table we can see that Yt = 1.5Y(t-1)-0.5y(t-2)

iii) So of we know the output of last 2 cycles then we can formulate an expression for the current cycle.

t Yt Y(t-1) Y(t-2) 2 64.25 64.5 65 3 64.125 64.25 64.5 4 64.0625 64.125 64.25 5 64.03125 64.0625 64.125 6 64.015625 64.03125 64.0625 7 64.0078125 64.015625 64.03125

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