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given utility function u=x0.5y0.5 where px=12 birr py=4 birr and the income of the consumer is M=240 birr.
a)draw the budget line.
b)what happens to the original budget line if the budget falls by 25%
c)what happens to the original budget line if the price of x doubles
d)what happens to the original budget line if the price of y falls to 2 birr
Please assist, Thank you
A firm has the following revenue and cost functions:
TR = 120Q – 2Q2
TC = 200 +60 Q + Q2
Determine the level of output at which the firm maximizes its total profit
Question 3: Suppose the inverse demand function for good X is given as P=100-2Q. Find
the price elasticity of demand when Q=40 units. What can you say about the type of the good
looking at the price elasticity of demand that you calculate in the first part?
The satisfaction gained by consuming x units of good 1 and y units of good 2 is measured by the utility function
U = 2x2 + 5y3
Currently an individual consumes 20 units of good 1 and 8 units of good 2.
(a) Find the marginal utility of good 1 and hence estimate the increase in satisfaction gained from consuming one more unit of good 1.
(b) Find the marginal utility of good 2 and hence estimate the increase in satisfaction gained from consuming one more unit of good 2
Suppose that the marginal rate of substitution is 2, the price of X is sh 3,and the price of Y is sh.1 a. If the consumer obtains 1 more unit of X, how many units of Y must be given up in order to keep utility constant? b. If the consumer obtains 1 more unit of Y, how units many of X must be given up in order to keep utility constant? c. What is the rate at which the consumer is willing to substitute X for Y? d. What is the rate at which the consumer is able to substitute X for Y ?
Suppose that a consumer consumes two goods X and Y and derives utility according the following utility function where U = 25X2/5Y 3/5 where α = 2/5 and β = 3/5 a. If Px is the price of good X and Py is the price of good Y and the consumer’s income is M. Derive the demand functions for the two goods X and Y b. If Px is shs 15 and Py is shs 10 and the consumer has shs.800 to spend on the two goods what are the optimal quantities of X and Y that maximize the consumer’s utility? c. Using the information in b above show that the values of α and β represent the proportion of the consumer’s income spent on good X and good Y respectively
A consumer must divide shs.250 between the consumption of product X and product Y. The relevant market prices are Px = shs 5 and Py = shs.10. a. Write the equation for the consumer’s budget line. b. Illustrate the consumer’s opportunity set in a carefully labelled diagram. c. Show how the consumer’s opportunity set changes when the price of good X increases to shs.10. How does this change the market rate of substitution between goods X and Y?
One most commonly used utility function is the Cobb-Douglas utility function which of the form 𝑼(𝑿, 𝒀) = 𝑿 𝜶𝒀 𝜷 where α and β are positive constants. a. Show that this function exhibits diminishing marginal utility for both goods X and Y (4mks) b. Show that the indifference curves of this utility function are convex (i.e show that is there is diminishing marginal rate of substitution between X and Y)
Explain, in plain words, what the R-square in this regression indicates. The demand function for good X is 𝐿𝑛𝑄𝑥 𝑑 = 𝑎 − 𝑏𝐿𝑛𝑃𝑥 + 𝑐𝐿𝑛𝑀 + 𝑒 . Where 𝑃𝑥 is the price of good X and M is income. Least squares regression reveals that â = 7.42 , bˆ = 2.81, cˆ =0.34, a. If M = 55,000 and 𝑃𝑥= 4.39, compute the own price elasticity of demand based on these estimates. Determine whether demand is elastic or inelastic. (4mks) b. If M = 55,000 and 𝑃𝑥= 4.39 , compute the income elasticity of demand based on these estimates. Determine whether X is a normal or inferior good
The demand function for good X is 𝑄𝑥 𝑑 = 𝑎 − 𝑏𝑃𝑥 + 𝑐𝑀 + 𝑒 . Where 𝑃𝑥 is the price of good X and M is income . Least squares regression reveals that â = 8.27, bˆ = 2.14, cˆ = 0.36, 𝜎â = 5.32, 𝜎𝑏ˆ = 0.41, and 𝜎𝑐ˆ = 0.22. The R-squared is 0.35. a. Compute the t-statistic for each of the estimated coefficients. (4mks) b. Determine which (if any) of the estimated coefficients are statistically different from zero. (4mks) c. Explain, in plain words, what the R-square in this regression indicates. (
