Given the consumption function C = a + bY (with a > 0 ; 0 < b < 1): (a) Find its marginal function and its average function. (b) Find the income elasticity of consumption ECY, and determine its sign, assuming Y > 0. (c) Show that this consumption function is inelastic at all positive income levels.
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Given the consumption function C = a + bY (with a > 0 ; 0 < b < 1):
(a) Find its marginal function and its average function.
(b) Find the income elasticity of consumption ECY, and determine its sign, assuming Y > 0.
(c) Show that this consumption function is inelastic at all positive income levels.
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- Given the consumption function C = a + bY (with a>0, 0 < b<1): a. find its marginal function and its average function. b. find the income elsaticity of consumption ECY, and determine its sign, assuming Y > 0. c. Show the income that this consumption function is inelastic at all positive income levelsDerive the expenditure function for the consumer and the hickson demand functionConsider the following linear demand function where QD = quantity demanded, P = selling price, and Y = disposable income: QD = -36 - 2.1P + .24Y. The coefficient of Y (i.e., .24) indicates that (all other things being held constant): * for a one percent increase in disposable income, quantity demanded would increase by 0.24 percent for a one unit increase in disposable income, quantity demanded would increase by 2.1 units for a one percent increase in disposable income, quantity demanded would decline by 2.1 percent for a one percent increase in disposable income, quantity demanded would decline by 0.24 percent
- According to studies undertaken by the U.S. department of agriculture, the price elasticity of demand for cigarettes is about +0.5. Suppose a major brokerage firm advised its clients to buy cigarette stock under the assumption that, if consumer income rise by 50 percent as expected over the next decade, cigarette sales would double. Based on the fundamental economic principles on income elasticity of demand, a reasonable reaction to this investment advice would be?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 a. Derive the Marshallian Demand for both goods, in terms of Income and the prices of both goodsConsider a simple, quasi-linear utility function: U(x,y) = x + ln y 1. Derive the uncompensated (Marshallian) demand functions for both x and y. 2. Compute the Indirect Utility Function and the Expenditure Function for this case.
- A consumer is faced with the followlling Utility Function, U( x 1 x2) = ( xp +xp ) 1/ρ, where 0<ρ<1. The consumer also faces the prices and and has income level m. 1. Set up the Lagrangian 0ptimisation function for the consumer and Compute the optimal consumption bundle for the consumer. 2. The solution in (a) represents the Marshallian demand function for and . Using the solution in (a) compute the indirect utility function. 3. Derive the corresponding expenditure function for the consumer and the Hicksian demand function.For each of the following utility functions, find the Marshallian demand function, the indirect utility function and the expenditure function. Assume that prices of x and x2 are p₁ and p₂ respectively and income is m. i) U(x1x2) = ln(x1+ x2) ii) U(x1x2) = (x1+ x2)Suppose James has a Cobb Douglas utility function of U = qaqa where q₁ = live music and q₂ = music tracks. Let a = 0.4 and label på the original price of qi and p2 the original price of q2. a. Derive expressions for James' optimal consumption levels of qı and q2 b. Derive James' expenditure function. Note: You will need to solve for U* and then derive an expression that relates U* to e(p, U), where e is the expenditure function for a given level of utility and prices pi and p2. Recall that Y = e(p, U") at qi and q2. For the remainder of the problem, let James have a monthly music budget of Y = $30 that he spends on qi and q2. Suppose that a new economic development policy is put in place in James' city that seeks to encourage arts and entertainment by subsidizing live music and that this causes the price of live music to decrease from pi = 1to pl = 0.5. The price of music tracks remains constant at p₂ = 1. C. Calculate the benefits that accrue to James from this new policy by…
- 3. (a) If the demand function is P = 60 – Qfind an expression for TR in terms of Q.Differentiate TR with respect to Q to find a general expression for MR in terms of Q. Hence write down the exact value of MR at Q = 50.Calculate the value of TR when (a) Q = 50 (b) Q = 51 and hence confirm that the 1 unit increase approach gives a reasonable approximation to the exact value of MR obtained in part (1)(b) The consumption function is C = 0.01Y2 + 0.8Y + 100 (i) Calculate the values of MPC and MPS when Y = 8.(ii) Use the fact that C + S = Y to obtain a formula for S in terms of Y. By differentiating this expression find the value of MPS at Y = 8 and verify that this agrees with your answer to part (a).The demand equation for a firm’s product has been estimated as Ln Qx = 7.3 – 2 Ln Px + 0.5 Ln I + 0.25 Ln Py - 1.5 Ln Pz, where Qx represents unit sales of brand X, Px is the price of brand X, I is per-capita income, Py is the price of brand Y, and Pz is the price of brand Z. (A)Write this demand equation in its multiplicative form. (B) What is the price elasticity of demand for brand X? is demand price elastic or inelastic? (C)What is the income elasticity of demand for brand X? What type of good is brand X?The demand equation for a firm’s product has been estimated as Ln Qx = 7.3 – 2 Ln Px + 0.5 Ln I + 0.25 Ln Py - 1.5 Ln Pz, where Qx represents unit sales of brand X, Px is the price of brand X, I is per-capita income, Py is the price of brand Y, and Pz is the price of brand Z. (A)Write this demand equation in its multiplicative form. (B) What is the price elasticity of demand for brand X? is demand price elastic or inelastic? (C)What is the income elasticity of demand for brand X? What type of good is brand X? (D)What is the cross-price elasticity of demand for brand X in relation to the price of brand Y? What is the relationship between brand X and brand Y? (E) What is the cross-price elasticity of demand for brand X in relation to the price of brand Z? What is the relationship between brand X and brand Z? (F) What effect will an increase in Px by 10% have on the firm’s total revenues? (G)What is the total effect will an increase in Px by 10%, a decrease in I…
