For the Utility function and demand functions: .0.5 U(x,y) = x05 +y I x(px, Py, 1) = y(px, Py, I) = ,0.5 Px(1+PxPy¹) I Px(1+px ¹py) 1. Calculate the elasticities of the Marshallian demand function for good 1.
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- Suppose that an individual has a Utility function represented by a CES function. The utility function of the individual is given as: U(x,y) = x1/2 + y1/2 b. Calculate the own price elasticity using the "share elasticity" of any good. Let us assume that the prices of both goods are equal.You are given the following utility function (and there is obviously an income constraint). Derive the Marshallian demand function (half the points) and identify the income elasticity of both goods (half the points). u=x1x2Consider an individual whose preferences are represented by the utility function U(x1,x2) = min {3x1+x2 , x1+3x2}. For this individual, Calculate her demand function X1* (P1, P2,m) Calculate her own price, cross price, and income elasticities at X1*(1, 2, 24) and at X1*(1, 4, 24). Based on these, can you say the goods 1 and 2 are (gross, or Marshallian) complements or substitutes?
- Given the utility function U = X0.5+Y0.5 and budget constraint I=Px X+ Py Y,(a) Is this utility function is homothetic?(b) Derive the consumer’s demand functions for goods X and Y.(c) Obtain the numerical values of the own-price elasticity, cross-price elasticity, and the income elasticity of demand for X and Y.(d) Derive the indirect utility function and the expenditure function for this consumer.e) Obtain the compensated demand functions for goods X and Y. (f) Prove that the Slutsky equation holds in this case.Suppose that the demand for a good is described by the inverse demand function p = 10 - 3q and the supply of the good is given by the inverse supply function p = 2 + 2 q: Q: What price will the buyers pay (use one decimal point)? Pb= [x]The demand for brownie dishes is q(p)=361,201-(p+1)^2 where q is the number of dishes they can sell each month at a price of p cents. Use this function to determine a) the number of dishes they can sell each month if the price is 50 cents, b)the number of dishes they can unload each month if they give them away, and c)the lowest price at which they will be unable to sell any dishes
- Sara’s demand function for good x is x(px,py,m) = m , where px is the 2px price of good x, py is the price of good y, and m is the income level. Is x a normal good at px = 1 and m = 24? Explore this by taking derivative of demand function with respect to m. Is x an ordinary good at px = 1 and m = 24? Explore this by taking derivative of demand function with respect to px.Assume that a 5 percent increase in income across the economy produces a 5 percent decrease in the quantity demanded of good X. The coefficient of income elasticity of demand is Multiple Choice positive, and therefore X is a normal good. negative, and therefore X is a normal good. positive, and therefore X is an inferior good. negative, and therefore X is an inferior good.Given utility function and prices of the good along with income U = x2 + y2 +2x + 2y P x = 1 P y = 1 M = 4 Find out ordinary demand functions and expenditure function.
- If the utility function for a consumer is defined by U=6X^0.6Y^0.7 . Given that the consumer's income is 300 currency units and unit price of goods X and Y are 12 and 15 currency units respectively, calculate the equilibrium quantity of both goods. Compute the price elasticity of demand for both goods and interpret your results. If income and prices of the two goods increase by 50%, calculate the equilibrium quantities of both goodsSuppose that a 10 percent increase in the price of normal good Y causes a 5 percent decrease in the quantity demanded of normal good X. The coefficient of cross elasticity of demand is Multiple Choice negative, and therefore these goods are substitutes. positive, and therefore these goods are substitutes. negative, and therefore these goods are complements. positive, and therefore these goods are complements..Based on sales data over the past year, the owner of a DVD store devises the demand function D1p2 = 40 - 2p, where D1p2 is the number of DVDs that can be sold in one day at a price of p dollars. a. According to the model, how many DVDs can be sold in a day at price of $10? b. According to the model, what is the maximum price that can charged (above which no DVDs can be sold)? c. Find the elasticity function for this demand function. d. For what prices is the demand elastic? Inelastic? e. If the price of DVDs is raised from $10.00 to $10.25, what is the exact percentage decrease in demand (using the demand function)? f. If the price of DVDs is raised from $10.00 to $10.25, what is the approximate percentage decrease in demand (using the elasticity function)?
