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- The table below shows the quantity of gasoline supplied by producers (Qs) and quantity of gasoline demanded by consumers (Qd) given certain price levels (P). 1. . Derive the Qd and Qs functions assuming that both variables are linearly related to price of gasoline. 2. Give the economic meaning of the slope of Qs and Qd functions.Answer the following questions using the following information. Columns 1 and 2 in the table below show the marginal utility that Cody gets by purchasing products A and B. Column 3 shows the marginal utility Cody gets from saving Assume that the price of A is $13 the price of B is $10, and Cody has an income of $129. a) Find the following series of MU/$ for each column. Note: Keep as much precision as possible during your calculations. Your final answer should be accurate to at least two decimal places Column 1 Column 2 Column 3 Units of A MU MU/S Units of B MU MU/$ Number of $ saved MU MU/S 68 6.8 1 80 6.15 1. 13 0. 2 71 5.46 2 63 6.3 2 10 0. 3 66 5.08 3 56 5.6 3 7 4 61 4.69 4. 46 46 0. 54 4.15 40 4 45 3.46 31 3.1 6. 1 39 3 22 2.2 0. 29 2.23 8 17 1.7 8 b) What quantities of A and B will Cody purchase in maximizing his utility? Quantity of A: 0 Quantity of B: 0 c) How many dollars will Cody save? Dollars Saved = $0 SAVE AND CLOSEThe function Q = F(p,ps,y) describes how the monthly demand, Q (measured in 100s of Widgets), for Grinch Inc. Widgets depends on the variables: • p = the price/Widget that Grinch Inc. sets (measured in $). • Ps= average price of substitutes for Grinch Inc. Widgets (measured in $). • y = average disposable income in the market for Widgets (measured in $1000s). When average disposable income in the market is $4200 and Grinch Inc.s price is $12 and the average price of substitutes is $11... ● Q = 66 •Op=-0.28 2ps = 0.52 ● Qy = 0.31 If average monthly income increases to $4400 and the average price of substitutes increases to $11.35, by approximately how much can Grinch Inc. increase their price while keeping demand for their Widgets fixed at Q = 66 ? Ο Δp = 0.87 O There is no way to estimate this from the given information.. Ο Δρ = 0.53 O Ap = 0.72
- A consumer's utility function is given by the expression: U = (0.6.x"s + 0.4Y"s)*. %3D • Determine the marginal utility functions for each commodity. Does marginal utility decrease when consumption increases? Assuming that the price of good X is Rs 15 and the price of Y is Rs 6, write the equation of the budget line and plot it when income is Rs 450. What is its slope? What does it indicate? • Calculate the marginal rate of substitution of Y for X and interpret its economic meaning. Write the equation showing consumer's equilibrium condition. Obtain the equilibrium values of X and Y. • Find the expressions for change in MUx due to increase in Y and change in MUy due to increase in X.Katie Kwasi's utility function is U(x₁, x₂)=5(In x₁)+x₂. Given her current income and the current relative prices, she consumes 10 units of x₁ and 15 units of x₂. If her income doubles, while prices stay constant, how many units of x₁ will she consume after the change in income? a)10 b)20 c)15 d)5The marginal utilities derived from the consumption of goods X and Y by a given consumer are given by MUx=40-6x and MUy=80-10y. If the prices of X and Y are Gh2 and Gh10 respectfully. determine the number of units of the commodities that the consumer must consume to optimize satisfaction granted that he/she earns an income of GH40 within the period.
- The expression, M = PXX+ PYY is called a budget constraint where M = amount of money available for expenditure; PX= price of commodity X; PY= price of commodity Y; PXX= expenditure on commodity X; PYY= expenditure on commodity Y. Use M = PXX+PYY to express Y as a function of X and note that the graph of this function is called a budget line. Algebraically derive: (1) the y-intercept; (2) the x-intercept. State what determines the slope of the budget line. Graph the function for M = 120; PX= 3; PY= 5 andshow what happens to the original budget line if M decreases by 25% with PX, PY constant.constraint optimization 1. a. use the substitution method. given the production function, Q=5k+3L+2KL, choose the input to maximized output subject to the constraint that the planned expanditure on input is 140 dollars. each unit of labour cost 4 dollars and each unit of capital cost 20 b. use the langrange multiplier given Z=4x2+3xy+6y2, subject to the constraint x+y=56A consumer’s utility function is given by the expression: ( )2 0.5 0.5 U = 0.6X + 0.4Y . • Determine the marginal utility functions for each commodity. Does marginal utility decrease when consumption increases?• Assuming that the price of good X is Rs 15 and the price of Y is Rs 6, write the equation of the budget line and plot it when income is Rs 450. What is its slope? What does it indicate?• Calculate the marginal rate of substitution of Y for X and interpret its economic meaning. Write the equation showing consumer’s equilibrium condition. • Obtain the equilibrium values of X and Y. • Find the expressions for change in MUX due to increase in Y and change in MUY due to increase in X
- The utility function of a certain consumer is U =(x1,x2)= x11/3 x22/3 , x 1and x 2 is the consumption of two kinds of goods, and the consumer's income is 100. The current prices of the two kinds of goods are P 1 =1 and P 2=2 respectively, ask: 1. If the price of the first commodity increases from 1 to 2, and other factors remain unchanged, what is the total effect of the price increase on the consumption of the first commodity? According to the Slutsky decomposition principle, what are the income effect and substitution effect? 2. Calculate the amount of income compensation that changes the price of the first commodity from 1 to 2, keeping the original effect unchangedThe demand for ice cream is a function of both the price of ice cream and the price of a substitute good, frozen yogurt. In particular the demand curve for ice cream, QP (P.c. Py) has the following 3. Suppose that the price of yogurt, Py, rises by $1. aqD two derivatives OPIC 5 and aPy a) Illustrate the impact of the rise of the price of yogurt on the ice cream market in your diagram. By how much would the demand for ice cream change at each price of ice cream given the rise in the price of yogurt? The market clearing price of ice cream, Pc, is the price at which the demand for ice cream equals C the supply of ice cream, QP (Pic, Py) = Q°(Pic) b) The market clearing condition above defines what kind of relationship between the market clearing price of ice cream and the price of yogurt? Use the market clearing condition to find the derivative of the relationship between Pic and Py IC c) Use the numerical values -5 and OPy 3 and your formula from part (b) to predict OPIC the change of…Consumers can choose between gas powered cars and electic cars. Suppose the price of gas increases by 25%. We can expect the price of electic cars to : Decrease Remain Unchanged Increase It is impossible to say