(a) Suppose that f is differentiable, positive and decreasing on [a, b] and has no critical points. If g(z) = | f(t) dt. Is g increasing or decreasing? Is g concave up or down?
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![(a) Suppose that f is differentiable, positive and decreasing on [a, b] and has no critical points.
If g(r) = | f(t) dt. Is g increasing or decreasing? Is g concave up or down?
(b) Economists study two functions: R(x)
and C(2) which are the revenue and cost when
r units of a product is sold or made, respectively.
The figure shows graphs of the R'(x) and C"(x)
for a certain manufacturer. Assume that R and
R'x)
2
C'x)
C are measured in thousands of dollars. What
does the shaded area in the figure represent?
50
100](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9df3b085-100b-4cd2-9bfb-b1044600736a%2F63e0784a-1644-4b40-b1d9-6f724cdd04e9%2Frc2o0t6_processed.jpeg&w=3840&q=75)
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- 2) (20) Demand for widgets is a linear function of price. If the price of Widgets is set to $20, 4200 widgets will be sold. If the price is raised to $25, demand falls to 3600 widgets. a) (4) Find the demand function D(x), where x represents the price and D(x)= y represents the demand for widgets. b) (2) Describe the meaning of the slope of the demand function, in the context of the price, and demand for widgets. c) (2) Find the revenue function R(x), which is price times the demand. (2) Graph the Revenue Function using Desmos, or any other graphing utility of your choice; note the scale on the axes. If your graph doesn't fit on the graph, your Revenue function is probably incorrect. Hint Ask Questions! Email! 100000 90000 80000 70000 60000 50000 40000 30000 20000 10000 y -5 20 25 30 35 40 45 50 55 60 65 e) (2) Give the meaningful domain for the revenue function. Use the criteria that one would not price widgets so low that one would pay to get rid of them. 5 10 15 (2)Calculate the…Problem #3 - Supply/Demand An potter sells handmade mugs on their website and has found that if the price for a mug is set at $22 they will sell 60 mugs and if they set the price at $35 they will only sell 21 mugs. You must show your work on all parts! a. Construct the monthly linear demand function. Use p for the price (dollars per mug) of the produce and q for the number of mug demanded. b. Find the equilibrium price if the monthly supply function is given by: q-0.003p² + 2p+10.5 Round to the nearest cent (i.e. $0.01). Include correct units. C. Report the monthly surplus or shortage when the price is $25. What is the corresponding revenue? Include correct units.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.
- 1. How does a consumer’s optimal choice of goods change if all prices and the consumer’s income double? (Hint: focus on the budget constraint) 2. Output is produced according to a production process given by: Q = 4LK, where L is the quantity of labor input and K is the quantity of capital input. If the price of K is $10 and the price of L is $5, then what is the cost-minimizing combination of K and L capable of producing 32 units of output?The manager of a hockey arena is pricing tickets for an upcoming game. She knows that if she increases the ticket price she will sell fewer tickets. The situation is modelled by the relation, R = -88.9p^2 + 2667p, where R is the total revenue and p is the ticket price, both in dollars. The graph is given.2) Daniel has the following Jineas Preferences over black tea be) and milk (y) (a) Setup the expenolituse minmization Problem for Daniel. what conditions, (BC) or(NNC) will necessarily be (b) Solve the expenditure Problem and obtain the Compensated and the Cost minimization function when binding at the oPtimum? ū = 40 and P = $6. c) Other Pic attach for Part(c)
- Suppose ABC Corp. spends $300,000 per year on some basic level of advertising, regardless of its revenues. In addition, the company spends 25 percent of each dollar of revenue on extra advertising. Write a mathematical equation that describes the functional relation between advertising (A) and revenue (R). A=??? (Enter your response as an expression.)The demand and supply functions for a particular commodity are D(x) = 80e-0.001x and S(x)= 30e0.001r , where x is the number of units of the product, D(x) is the price that results in a consumer demand of x units and S(x) is the price that results in a producer supply of x units. a. Find the equilibrium point using your calculator and identify the equilibrium units and price. Give your answers to the nearest whole unit and nearest dollar. The value of x at equilibrium is units. The value of p at equilibrium is b. Determine the consumers' surplus.Input either "increase" or "decrease" where relevant: A decrease in the price of a complementary good will cause its complement’s equilibrium price to ...... and the equilibrium quantity to .....
- Ammongas´'s demand depends on many factors, but can be presented in simplified form as: P = 8,000,000 - 240,000 * Q, where “Q” are standard plants sold per. year. Make a graphic illustration of the P-function, where it applies that the price can not be negative and a negative number of plants can not be demanded. Then derive the TR function and the MR function mathematically.Trump, Part 1. Donald Trump has preferences over private helicopters (x) and designer wigs (y) given by u(x, y) = 2ln(x) + 5ln(y). The costs of these goods are, respectively, px = 10 and py = 5, and The Donald’s income is I = 30. (a) Write the Langrangian for Trump’s optimization problem and derive the first order conditions. (b) Find Trumps’s optimal consumption of helicopters x ∗ and wigs y ∗ and derive an algebraic expression for his income expansion path (IEP). (c) Graph the budget constraint, IEP, and optimal bundle (x ∗ , y∗ ).Assume that the market supply curve for potatoes is Qs1 = 12 + 0.5P, and that there are two marketing periods for the crop. In the first marketing. The demand curve is Qd1 = 24-P1, and the second period it is: Qd2 = 18- P2. draw a graph of the markets in the two. Showing prices and quantities if it cost nothing to store potatoes. Be sure to label all the relevant features on your graph.
