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Find 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=48
5. U(x,z)=a2z3 and3a+2z=36
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- Assuming, there are two goods: Coffee and Tea. Your budget is 18,000 KRW per day. The price of Coffee ranges between 0 KRW to 6,000 KRW. The price of Tea ranges between 0 and 5,000 KRW Specify your indifference map of your preference relation Specify your utility function Specify a budget constraint based on the assumption above Specify your own-price offer curves for coffee Specify your curve Engel curve for coffeeAssuming, there are two goods: coffee and tea. Your budget is 18000 KRW per day. The price of coffee pc ranges between 0 KRW to 6000 KRW The price of tea pt ranges between 0 and 5000 KRW a) Specify your indifference map of your preference relation b) Specify your utility function c) Specify a budget constraint based on the assumption above d) specify your own-price offer curves for coffee e) specify your curve Engel curve for coffeeFind the optimal bundle using the following utility functions and budget constraints. 1. U(x1,x2)=3x1+2x2 and6x1+2x2 =242. U(x1,x2)=x1+2x2 and3x1+6x2 =483. U(x1,x2)=min{x1,x2}and4x1+2x2 =484. U(x1,x2)=min{4x1,2x2}and2x1+3x2 =36
- 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.A consumer currently spends a given budget on two goods, X and Y, in such quantities that the marginal utility of X is 15 and the marginal utility of Y is 8. The unit price of X is $3 and the unit price of Y is $2. The utility-maximizing rule suggests that this consumer should Multiple Choice a. decrease consumption of product X and increase consumption of product Y. b. increase consumption of product X and increase consumption of product Y. c. decrease consumption of product Y and increase consumption of product X. d. stick with the current consumption mix because it yields maximum utility.