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Course: Calculus 1
I. Define supply function indicating whether it is INCREASING or DECREASING by means of a graph.
II. Define demand function indicating whether it is INCREASING or DECREASING by means of a graph.
III. Define total cost function (TC), total revenue (TR), utility (U), and what is relationship between these 3 functions.
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- Describe the equilibrium conditions in consumer theory (utility maximization) and in production (output maximization). How are they similar? Briefly talk about the duality between production and cost. (Don't forget to talk about law of diminishing MU, diminishing MRS, diminishing MPs and diminishing MRTS. Clearly define each concept with examples. Make sure to define budget and cost constraints. Indifference curves and isoquants. Graphically derive the equilibrium conditions. Make sure to talk about how output maximization and cost minimization lead to the same maximizing/minimizing input bundles. )Part 2: Storage Equilibrium 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 period the demand curve is: QD1 = 24 – P1, in the second period it is: QD2= 18 - P2. Draw a graph of the markets in the two periods showing prices and quantities if it costs nothing to store potatoes. Be sure to label all the relevant features on your graph. [Insert an image of your graph here] Show the prices and quantities in each period if it costs $5 per cwt. to store potatoes for delivery in the second marketing period. Again, be sure to label all relevant features on your graph (s). [Insert an image of your graph here] By comparing the results for 5 and 6 above explain how the cost of storage affects prices and quantities in each period.What is the relationship between the demand curves derived from cost minimization ,and demand curves derived from utility maximization? Show your answer graphically andalgebraically by considering two goods, i=1,2
- Spreadsheet exercises. Suppose that the market for video games is competitive with demand function Qd = 130 − 4p + 2Y + 3pm − 2pc, where Qd is the quantity demanded, p is the market price, Y is the monthly budget that anaverage consumer has available for entertainment, pm is the average price of a movie, and pc is the price of a controller that is required to play these games. 1. Given that Y = $100, pm = $30, and pc = $30, use Excel to calculate quantity demanded for p = $10 to p = $80 in $5 increments. Use Excel’s charting tool to draw the demand curve. 2. Now, Y increases to $120. Recalculate the demand schedule in part 1. Use Excel’s charting tool to draw the new demand curve in the same diagram. 3. Let Y = $100 and pc = $30 again, but let pm increase to $40. Recalculate the demand schedule in part 1. Use Excel’s charting tool to draw the graph of the new demandcurve. 4. Let Y = $100, pm = $30, and pc increase to $40. Recalculate the demand schedule in part 1 and use Excel to draw…Scenario 1: Suppose you are a salesperson is a high end clothing store known for its personal service. You receive a salary plus a commission equal to 10% of the sales/revenues that you sell. The manager of your store informs you that prices of the clothing in your store will increase by 10%. (1) Assuming everything else remains the same, would you be happy or sad about the price increase? Explain why or why not. Scenario 2: Suppose you are a salesperson at Macy’s, a department store. You receive a salary plus a commission equal to 10% of the sales/revenues that you sell. Macy’s informs you that price of the clothing in your store will increase by 10%. (2) Assuming everything else remains the same, would you be happy or sad about the price increase? Explain why or why not.Indifference curve assumption where consumers aim to maximise utility given income andprices of products is called ________________________assumption.A. Ordinal util.B. Non-satiety.C. Rationality.B. Transitivity2. Economic profit =A. Total Revenue – Explicit costs.B. Total Revenue – Total costs.C. Total Revenue – Implicit Cost.D. Total Revenue – Opportunity cost.3. _____________________is a firm that owns, controls and manages assets in many countries.A. Sole trader.B. Partnership.C. Multinational firm.D. Monopoly.4. Which one of the following is remuneration for capital?A. Wages.B. Interest.C. Profit.D. Rent 5. ____________________is market structure with one single seller.A. Monopolistic competition.B. Monopoly.C. Perfect competition.D. Oligopoly.6. Complete the following table to answer question 6: Quantity of oranges Total utility Marginal utility 0 0 1 10 2 25 3 31 4 35 5 37 6 33 At which level of…
- Non-linear pricing in water utilities: You are the manager of water utilities, and you are trying to determine how different water pricing schemes will affect consumption. One option for pricing is called decreasing block pricing, where the marginal price paid decreases with quantity paid. In particular, you are considering a decreasing block schedule where consumers pay $0.20 per gallon for the first 20 gallons consumed, and then $0.10 per gallon for any additional gallons consumed. For this decreasing block pricing scheme, draw the budget constraint for a consumer that has $10 of income, where the composite good is the good on the y-axis. Another option for pricing is called increasing block pricing, where the marginal price paid increases with the quantity paid. In particular, you are considering an increasing block schedule where consumers pay $0.20 per gallon for the first 20 gallons consumed, and then $0.40 per gallon for any additional gallons consumed. For this increasing…Suppose you offer a quantity discount: first 10 cupcakes at $3 each and any cupcakes over 10 are offered at a discounted price. What discount price will maximize your profit? Show this quantity discount arrangement on your graph and shade areas representing your profit and CS.Suppose that the total revenue function of a firm is defined as TR= (P)(Q) where TR= f(Q). The usual notation applies. 1. Given its total revenue function, solve for the maximum revenue that the firm can earn. How many units of output should the firm sell to earn that amount of revenue? Note: Solve the problem using simple algebra only. Do not differentiate. 2. What are the roots of the total revenue function? Interpret economically.
- Description 1. Suppose the utility function for goods x and y is given by utility = U(x, y ) = xy + y. a. Calculate the uncompensated (Marshallian) demand functions for x and y, and describe how the demand curves for x and y are shifted by changes in I or the price of the other good. b. Calculate the expenditure function for x and y. c. Use the expenditure function calculated in part (b) to compute the compensated demand functions for goods x and y. Describe how the compensated demand curves for x and y are shifted by changes in income or by changes in the price of the other good.Rahim runs a fruit stand where he sells apples and mangoes. Each apple costs BDT 5.00 per piece and each mango costs BDT 8.00. The demand for apples and bananas are described by the following functions, where Pa, and Pm denotes the price of apples and bananas.Qa= 300-5Pa+ 3Pm Qm = 3Pa – 2.5Pm What prices of mangos and apples Rahim should set in order to maximize profit?Suppose the supply function for product X is given by QXS = − 30 + 2Px − 4Pz. Instruction: Enter all values as integers, or if needed, a decimal rounded to one decimal place.a. How much of product X is produced when Px = $600 and Pz = $60?b. How much of product X is produced when Px = $80 and Pz = $60?c. Suppose Pz = $60. Determine the supply function and inverse supply function for good X. Graph the inverse supply function. Supply function: Inverse supply function: Graph the inverse supply function from QX = 0 to QX = 200
