Econ Question

Why doen’t this question make sense to me? I know its easy when I see the answer but for some reason I keep getting it wrong. Its like it should be an inequality or something that can be solved for. Can someone please explain an easy way to solve this that makes sense? Thanks. Flash Flight produces running shorts in a monopolistically competitive market. It sells no shorts at $50 a pair. With their current advertising budget, each $5 drop in price results in an increase of 20 shorts sold per day. If the firm doubles their advertising budget, they can triple the quantity of shorts sold at each price. The firm’s marginal cost is constant at $5 a pair. What quantity of shorts will maximize profits for Flash Flight? a. 90 pairs per day. b. 180 pairs per day. c. 270 pairs per day. d. 540 pairs per day.

Not sure if this is correct, but here is my thought process P=MC --> P=5, MC =5 At P=5, the firm sells [(50-5)/5]*20= 180 pairs of shorts

that’s what I got at first, Stalla says: Choice “a” is correct. Profits are maximized when Flash Flight produces the quantity at which marginal cost equals marginal revenue. Marginal cost is constant at $5 a pair. If demand for the firm’s running shorts at $5 is 180 pairs per day, then marginal revenue at $5 is 90 pairs per day. (Marginal revenue curve lies halfway between the y-axis and the demand curve.) Therefore the profit maximizing quantity is 90 pairs per day. It makes sense if you put it all in a table, but for some reason this is not intuitive at all to me.

I misread that and thought it said perfect competition. That makes sense. I think I need to lay the books to rest tonight…

Ooops I misread that and thought it said perfect competition. That makes sense.

how do you know that the MR curve lies exactly halfway between the y-axis and the demand curve?

How are people factoring the incremental benefits of advertising?

I emailed Stalla about this question, here is the answer provided: The marginal cost curve will in all cases not necessarily lie half-way between the y-axis and the demand curve. That bit of information is not really needed to answer this question. The key concept in profit maximization is finding where marginal cost equals marginal revenue. Questions on perfect competition, monopolistic competition and unregulated, non-price discriminating monopolists will be structured as graphs where you will be required to identify the profit-maximizing price and level of output, or as tables of price and cost data that will ask you to determine those values from the data given. In all cases, profits are maximized at the level of output where marginal cost equals marginal revenue. In a case of perfect competition the price is given by the market. In cases where the firm faces a downward-sloping demand curve, such as monopolistic competition and unregulated monopoly, you find the market-clearing price on the demand curve consistent with that level of output. Exceptions to the MC = MR rule include some situations in oligopoly, regulated monopolies, and price-discriminating monopolies. This answer is pretty generic and doesn’t explicitly address this question. Is there a mathematical approach to solving this problem?

mcf Wrote: ------------------------------------------------------- > How are people factoring the incremental benefits > of advertising? They don’t. Not if they are selling at MR = MC. There is no additional gain from each additional output so why increase fixed advertising costs?

As some others have posted, I’d also be interested if anyone has a good mathmatical equation way to represent this.

intuitively y=mx+b for the demand curve slope we know that m = -5/20 since the slope of the MR curve is always twice the slope of demand the MR m= -10/20 b=$50 (y intercept since zero shorts are sold at $50) since profits are maximized when MR=MC solve for y=$5 $5 = -10/20(x) +$50 x= 90

Thanks – very helpful, except I don’t follow this one line… “since the slope of the MR curve is always twice the slope of demand the MR m= -10/20”

Why MR is always twice as demand?

Revenues will be maximized when the optimal quantity of goods is sold at the optimal price. Think if the demand curve. At what quantity Q are revenues maximized? Draw a demand curve and think of it geometrically. Revenue is represented at Price x Quantity, or in other words the base times the height of the largest square (or rectangle) you can fit under the demand curve. when demand is represented as a straight line (no matter the slope) the largest square (highest revenue) will be bounded by the x and y axis and a point on the demand curve. Again think geometrically on how to “fit” the largest square… if the demand line crosses the x axis at 10 units, half that distance from the origin (i.e. 5 units) will be the right bound of the revenue “box”… another way to get to the 5 unit point is to increase the slope of the demand line to be twice as steep in order to bisect the origin (0,0) and the point where the demand line crosses the x axis (10,0)… this MR line will cross at (5,0) this is difficult explain without having the ability to draw some lines… and apologize if this further confused anyone… perhaps a quick google search on MR curves will illustrate the relationship better. these may help. this can all be explained with calculus as well.

Now use a little calculus, I finally got why MR is alway twice as demand: The demand function is: P=aQ + b Then the revenue is: R=PQ = aQ^2 + bQ The marginal revenue: MR = dR/dQ = 2aQ + b So the MR is always twice as the demand.

Also, MR is not always twice demand. It all depends on the price function. Suppose P = a(Q^2) + b. TR = a(Q^3) + b(q) TR = 3a(q^2) +b To solve this problem mathematically using monopolistic competition, you set MR = MC to find quantity. As written about, MR is the first derivitave of TR. In this case: TR = X*P, where X = Q / 20. P = 50-5*X TR = 50X - 5*(X^2) MR = 50 - 10X MC = 5 10X - 50 = 5 10X = 45 X = 4.5 Q = 4.5 * 20 = 90 Another way to look at this problem is to use trial and error to find where profit is the highest. P = TR - TC TR was already calculated. TC = 5X 50X - 5(X^2) - 5(X) = Profit a) X = 90/20 = 4.5 ------ Profit = 101.25 B) X = 180/20 = 9 ------ Profit = 0 C) X = 270 / 20 = 13.5 — Profit = -303.75 D) X = 540 / 20 = 27 ----- Profit = -2430