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- When utility function U(q1, q2)=min{ 34.6 q1, 17 q2} and q1= 33 and q2= 60 are given, find utility level consumer gains?Q1-Select the true or false for the following statement also give the explanation and support your answer with graphical presentation where necessary. Explanation is compulsory 3 to 6 line. If total utility at optimum level marginal utility is negative.You are given the following utility function and price of commodities q1 and q2: U = 3q1+q1q2-5q2-15 P1=3 and p2=2 If the corresponding bugdet is 20. i. Write the consumer's budget equation,augmented objective function, ii.construct a constrained utility maximization problem out of the information given above, Is the second order condition for a maximum satisfied? Iii. Find the optimum level of U and the levels of q1 and q2 that will satisfy the first order condition for a maximum.
- Brit-Brick is a company that produces bricks and cement in the UK. Their largest consumer is ConstrUK, a UK construction company. The manager of Brit-Brick has asked the research department to find out how sensitive ConstrUK’s demand for bricks is. The research department has estimated that ConstrUK’s preferences over bricks (x) and cement (y) can be described by the utility function U(x,y)=xb/10y1-b/10 where b is 2, and where x and y are measured in bags. Example: if b=4, then . U(x,y)=x4/10y1-4/10=x2/5y3/5 The price for one bag of cement is equal to £1. It is estimated that ConstrUK’s budget is £10,000. Find the price-consumption curve for bricks and the corresponding demand curve.For the utility function U = Qx0.31Qy(1-0.31) find the trade-off rate between good X and good Y at Qx= 7 and Qy=17 Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 = 1.2, 1.14 = 1.1).An agent has income m that can be spent on frequent flier miles f or on other goods – a “composite good” g. Their respective prices are: pf = 10 per mile and pg = 1 per unit. The flier miles have a stepwise price schedule. After the first 25 miles the price is reduced by 20% and after 50 miles the price is further reduced by another 50%.1. Put g on the vertical axis and f on the horizontal axis. Assume m = 200, and draw the budget constraint with all the intercepts and appropriate slopes. 2. On a separate graph, repeat part (1) for m = 300. 3. On a separate graph, repeat part (1) for m = 600.
- Q1 (b) – each graph needs to be approximately half page in size. All the axis need to be labeled. The TU values need to be scaled as follows: 10, 20, 30, 40, 50, 60 – with 2 cm gaps. The MU values need to be scaled as follows: -5, 0, 5, 10, 15 – with 2 cm gaps. b) Using the values from the above table, “Plot” (on separate graphs) i) Total Utility ii) Marginal Utility graphsFind the optimal bundle using the following utility functions and budget constraints. 1. U(x,y)=lnx+yand2x+y=10 2. U(x,y)=3x+2yand3x+2y=24 3. U(a,z)=3a+2zand3a+6z=24 4. U(a,z)=a2z2 and4a+2z=485. U(x,z)=a2z3 and3a+2z=36Mats, who has reference-dependent preferences over beer and money, goes to the local pub with a friend, but is not planning on drinking any beer or spending any of his 50 Euro in cash. Let his end-of-evening outcomes in pints of beer consumed and cash be c1 and c2, respectively, and let his reference point in pints of beer and cash be r1 and r2, respectively. Then, Mats’ utility is given by v(6c1 − 6r1) + v(c2 − r2), where v(x) = x for x ≥ 0, and v(x) = 1.5x for x < 0. (a) Suppose that the price of beer is pB. Calculate Mats’ utility from drinking one pint of beer at this price. What is Mats’ utility from drinking no beer? And, comparing these two utility values, what is the maximum price pB that Mats would pay for one beer? (b) Suppose that Mats unexpectedly gets a pint of beer as part of a promotion at the pub, and incorporates its consumption into his reference point in beer. [Hint: this means that (r1, r2) = (1, 50).] Suppose that Mats could sell the beer at a price pS.…
- A young consumer has to decide how to spend his spare time. He can either watch movies x or play online video games y. Each round of the game cost 20 and each movie cost 20. He has 200 dollars to spend each week. In addition, he has time constraint. He can spend no more than 20 hours for entertainment each week. A movie last 2 hours and playing a game takes about 1 hour. His utility is given by √xy. Use the Kuhn-Tucker condition to find his optimal choice. (Assume that x and y can take any value, not necessarily integers.) Does the solution satisfy the necessary and sufficient condition for a maximum?1. Use budget constraints to express consumption levels, ct and ct+1. (Hint: Use income conditions given above in the budget constraint. Notice that there are two possible states in the second period.)2. Rewrite the utility maximization problem as choosing the optimal at alone. (Hint: Replace ct and ct+1 in the utility function with your answers from point 1. Use probabilities to derive the expected value in the utility function. Remember that a random variable that takes values x1 in state one with probability p and x2 in state two with probability 1 − p has the expected value E [x] = p.x1 + (1 − p).x2)3. Derive the first order condition and find the optimal value of savings, at. (Hint: The only control (choice) variable is at)4. Does household accumulate precautionary savings to self-insure against the scenario of low income in the second period? Why or why not?True/False Utility refers to the total satisfaction or happiness that an individual get from consuming a product.
