Assume that you are a borrower, and the interest rate decreases. Draw a diagram illustrating this scenario. Determine whether the substitution and income effects have the same sign, or opposite signs. [Hint: it will be easier to draw a diagram if your initial endowment is such that more of their income arrives in period 2. E.g. y = (200,400)]
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- 1. Complete the following table and answer the questions below: Units consumed Total utility Marginal utility 1 10 10 2 8. 25 4 30 5 6. 34 2. Columns 1 through 4 in the table below show the marginal utility, measured in utils, that Ricardo would get by purchasing various amounts of products A, B, C, and D. Column 5 shows the marginal utility Ricardo gets from saving. Assume that the prices of A, B, C, and D are P18, 6, 4, and 24, respectively, and that Ricardo has an income of 106. Column 1 Column 2 Column 3 Column 4 Column 5 Unit Unit Unit Unit No. of MU MU MU MU P saved MU of A of B of C of D || || || || | 1 72 1 24 1 15 1 36 1 2 54 2 15 12 2 30 2 3 45 3 12 8 3 24 3 36 4 18 2 27 5 7 5 13 5 1 18 6. 7 6. 1/2 7 15 7 7 3.5 7 4 7 1/4 8 12 8. 1 8 2 8. 1/8 a. What quantities of A, B, C, and D will Ricardo purchase in maximizing his utility? b. How many pesos will Ricardo choose to save?25 Columns 1 through 4 in the following table show the marginal utility, measured in utils, that Ricardo would get by purchasing various amounts of products A, B, C, and D. Column 5 shows the marginal utility Ricardo gets from saving. Assume that the prices of A, B, C, and D are, respectively, $9, $3, $2, and $6 and that Ricardo has an income of $71. Column 1 Column 2 Column 3 Column 4 Column 5 Units of Good A Units of Units of Units of MU MU MU MU Good B Good C Good D Number of Dollars Saved MU 1 72 1 24 1 15 1 36 1 5 2 54 2 15 2 12 2 30 2 4 3 45 3 12 3 8 3 24 3 3 4 36 4 9 4 7 4 18 4 2 5 27 5 7 5 5 5 13 5 1 6 18 6 5 6 4 6 7 6 0.50 7 15 7 2 7 3.5 7 4 7 0.25 8 12 8 1 8 3 8 2 8 0.13 Instructions: Enter your answers as a whole number. a. What quantities of A, B, C, and D will Ricardo purchase in maximizing his utility? 4 units of A 3 units of B units of C units of D b. How many dollars will Ricardo choose to save?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.
- 1. [35 marks] An individual derives utility from consumption spending C and leisurel according to the following utility function: U(C,1)=C"1¹-a where 0>x>1. Leisure time in hours is given by: 1=T-H where T is hours of total time available and H is hours of work. The consumer's real income is given by: C=w (T-1)+N where w is real wage and N is real non-labour income. a) Derive the optimal values of C, I and the Lagrangian multiplier if the individual wishes maximise utility subject to the to constraint: C=w (T-1)+N. [15 marks]Suppose you expect to earn $10 this year and $10 next year. Each dollar you earn this year can be either spent, or saved at an interest rate of 10%. If you want to spend more than $10 this year, you can borrow money at 10% interest and repay it next year. Next year, you plan to pay oyour debts (if any), then spend all your earnings and all your savings (if any). Draw your budget line between “dollars spent this year" and “dollars spent next year". Suppose the government imposes a 50% income tax on all your earnings this year and next year (not including your interest earnings). Draw your new budget line. Suppose the government imposes a 50% sales tax on everything you buy this year and next year. Draw your new budget line. Suppose the government imposes a 50% income tax on all your earnings this year and next year, including your interest earnings. Draw your new budget line. True or False: If interest earnings are not subject to income tax, then an income tax and a sales tax…5. Suppose there are 12000 individuals in an economy. All of them have the same preferences, represented by the following utility function: u(x1, x2) = x1x2 where a, is individual consumer's consumption on housing, and r2 is individual consumer's consumption on everything else except housing. Suppose there are 2000 consumers with income $200 each, 3000 consumers with income $160 each, and 7000 consumers with income $60 each. Derive the market demand for housing.
- Jien is just bored all the time; no amount of success makes him happy, it seems. Below is a list of his income for the last several years and the utility he experienced per dollar of income: Year Yearly Income Utility per Dollar Earned 2017 $60,000 2 utils 2018 $70,000 1.8 2019 $100,000 1.5 2020 $120,000 1 2021 $145,000 0.40 From the above, we can say that Jien most likely is different from most people economists study in terms of risk attitudes is "risk loving" will not take a fair bet has a utility of wealth curve that is a straight line2. [For this question, the unit used is in thousands of Rupiah].Rihana's preferences for consumption (C) and leisure (L) are explained by the utility function:U(C, L) = (C - 200) (L - 56) so the marginal rate of substitution is MRS = (L - 56)/(C - 200) If Rihana has 168 hours to devote her time to work or leisure per week and she receives Rp. 240 of the pension fund per week, how much is Rihana's reservation fee? (A). Rp. 0(B). Rp. 2.80(C). Rp. 5.00(D). Rp. 6,25(E). Minimum wage rate. Choose one of the answers from the five choices provided. And please, also provide a brief description, explanation or argument for your choice. Thank you Bartleby!Columns 1 through 4 of the accompanying table show the marginal utility, measured in utils, that Ricardo would get by purchasing various amounts of products A, B, C, and D. Column 5 shows the marginal utility Ricardo gets from saving. Assume that the prices of A, B, C, and D are $18, $6, $4, and $24, respectively, and that Ricardo has an income of $105. Column 1 Column 2 Column 3 Column 4 Units Units Units Units of A MU of B MU of C MU of D MU 1 72 1 24 1 15 1 36 54 15 12 2 30 3 45 3 12 3 8. 3 24 4 36 4 7 4 18 27 7 5 5 13 6 18 6 5 6 4 6 7 7 15 7 2 7 3.5 7 8 12 8 1 8 3 8 2 а. What quantities of A, B, C, and D will Ricardo purchase in maximizing his utility? b. How many dollars will Ricardo choose to save? c. Check your answers by substituting them into the algebraic statement of the utility-maximizing rule. In other words, show it works when using this rule.
- Columns 1 through 4 in the following table show the marginal utility, measured in utils, that Ricardo would get by purchasing various amounts of products A, B, C, and D. Column 5 shows the marginal utility Ricardo gets from saving. Assume that the prices of A, B, C, and D are, respectively, $18, $6, $4, and $24 and that Ricardo has an income of $106. a. What quantities of A, B, C, and D will Ricardo purchase in maximizing his utility? b. How many dollars will Ricardo choose to save? c. Check your answers by substituting them into the algebraic statement of the utility-maximizing rule.Brian earns income equal to $82,000 in the first period, but his income will drop to $19,170 in the second period. a. Sketch his intertemporal budget constraint, assuming a 6.5% interest rate. Add an indifference curve that assumes he optimally chooses to save $40,000 in the first period. Be sure to CLEARLY graph your answer, with labels on the axes and any other important points. Also show work for any calculations done. b. Show the effect of a 50% tax on interest income, assuming the substitution and income effects cancel each other out. Again, be sure to clearly graph your answer and show work for any calculations done.5. The CES function f defined for K > 0, L > 0, by f(K, L) = A(SKP + (1-6)L-P), where A > 0, p = 0, 0≤ ≤ 1. Show that function f is concave if p > -1 and convex when p ≤ -1.