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A consumer chooses x1 and x2 to maximize U(x1,x2) = log x1 + log x2, subject to the budgetconstraint: px1 + x2 = y (note that the price of x2 has been normalized to equal one).
Solve the budget constraint for x2 as a function of x1. Using the substitution method, convert the consumer's optimization problem into a one-dimensional maximization problem, and find the consumer's optimal level of x1 as a function of p and y. Do the same for x2. After, solve the consumer's optimization problem using the Lagrange multiplier method. Interpret the first-order conditions in terms of the slope of budget constraint and indifference curves.
After the firm's patent expires, predict the new market output and price. (Assume that competing suppliers have the same economic costs as the original producer.) Compute the resulting change in consumer surplus.
Let MUA = z = 10 ? x and MUB = z = 21 2y, where z is marginal utility per dollar measured in utils, x is the amount spent on product A, and y is the amount spent on product B. Assume that the consumer has $10 to spend on A and B-that is, x + y = 1..
The utility estimates that by switching to gas, it will save $22,000 per year, starting 3 years from now. At an interest rate of 8% per year, determine the present worth in year 0 of the projected savings that will occur in years 3 to 10.
Solve the following linear programming model graphically. In addition, write the problem in standard form and do a constraint analysis for the optimal solution. Minimize 10x + 15y Subject to 5x + 2y ? 40 x + 2y 0
Using the midpoints formula presented in the text, calculate the elasticity coefficient for each price level, starting with the coefficient for the $4 to $6 level. For each coefficient, indicate what type of elasticity is indicated, elastic demand..
the industry demand function for bulk plastics is represented by the following equation p = 800 - 20Q where Q represents millions in pounds of plastic the total cost function for the industry, exclusive of a required return on invested capital is ..
assume that the government decides toreduce spending and taxes and so G = T = 274.16. What value mustthe central bank set for M in order to keep the price levelconstant following the government downsizing
A current asset (defender) is being evaluated for potential replacement. It was purchased four years ago at a cost of $62,000. It has been depreciated as a MACRS (GDS) five-year property- class asset. The present MV of the defender is $12,000.
a safe firm and a risky firm. Each firm needs to borrow the same amount of funds to start a project. The safe firm knows with certainty that it will see a 30 percent return on the project (i.e., for each $100 borrowed, the safe firm will see rev..
Bella can produce either a combination of 60 silk roses and 80 silk leaves or a combination of 70 silk roses and 55 silk leaves. If she now produces 60 silk rose 80 silk leaves, what is the opportunity cost of producing additional 10 silk roses
The amount of water consumed each day by a healthy adult follows a normal distribution with a mean of 1.54 liters. A sample of 10 adults after the campaign shows the following consumption in liters: 1.35 1.68 1.76 2.00 1.84 1.84 1.50 1.82 1.86 1.6..
The plant has a capacity output of 200,000 calculators per year, and the plant's manager regards 75 percent of capacity as the normal or standard output. The projected total variable costs for the normal or standard level.
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