Intermediate Microeconomics Ch 1 Example: TV and radio ads Katherine M. Sauer, Ph.D. Besanko & Braeutigam’s Microeconomics 4 th ed

You are a product manager at a microbrewery and have $1 million advertising budget to allocate between TV and radio ads for the next year. Table 1.1: Advertising and New Beer Sales Generated (in barrels per year) Total Spent Sales from TV ads Sales from Radio ads $000 $100,0004, $200,0009,0001,800 $300,00012,7502,550 $400,00016,0003,200 $500,00018,7503,750 $600,00021,0004,200 $700,00022,7504,550 $800,00024,0004,800 $900,00024,7504,950 $1,000,00025,0005,000 If you spent $200,000 on TV ads, you’d expect to get 9,000 new sales. If you spent $200,000 on radio ads, you’d expect to get 1,800 new sales.

Total Spent Sales from TV ads Sales from Radio ads $000 $100,0004, $200,0009,0001,800 $300,00012,7502,550 $400,00016,0003,200 $500,00018,7503,750 $600,00021,0004,200 $700,00022,7504,550 $800,00024,0004,800 $900,00024,7504,950 $1,000,00025,0005,000 Suppose you spend $400,000 on TV ads and the rest on radio ads. Your total new sales would be: 16, ,200 20,200 barrels

If your goal is to maximize new sales, how should you allocate the advertising budget? Total Spent Sales from TV ads Sales from Radio ads $000 $100,0004, $200,0009,0001,800 $300,00012,7502,550 $400,00016,0003,200 $500,00018,7503,750 $600,00021,0004,200 $700,00022,7504,550 $800,00024,0004,800 $900,00024,7504,950 $1,000,00025,0005,000 The “obvious” answer is to spend all $1,000,000 on TV ads and get 25,000 new sales. But, this is not the optimal allocation!

Total Spent Sales from TV ads Sales from Radio ads $000 $100,0004, $200,0009,0001,800 $300,00012,7502,550 $400,00016,0003,200 $500,00018,7503,750 $600,00021,0004,200 $700,00022,7504,550 $800,00024,0004,800 $900,00024,7504,950 $1,000,00025,0005,000 If you spent $900,000 on TV ads you would generate 24,750 new sales from TV and the $100,000 you spend on radio would generate 950 new sales for a grand total of 25,700 new sales.

Total Spent Sales from TV ads Sales from Radio ads $000 $100,0004, $200,0009,0001,800 $300,00012,7502,550 $400,00016,0003,200 $500,00018,7503,750 $600,00021,0004,200 $700,00022,7504,550 $800,00024,0004,800 $900,00024,7504,950 $1,000,00025,0005,000 If you spent $800,000 on TV ads you would generate 24,000 new sales from TV and the $200,000 you spend on radio would generate 1,800 new sales for a grand total of 25,800 new sales.

Total Spent Sales from TV ads Sales from Radio ads $000 $100,0004, $200,0009,0001,800 $300,00012,7502,550 $400,00016,0003,200 $500,00018,7503,750 $600,00021,0004,200 $700,00022,7504,550 $800,00024,0004,800 $900,00024,7504,950 $1,000,00025,0005,000 If you spent $700,000 on TV ads you would generate 22,750 new sales from TV and the $300,000 you spend on radio would generate 2,550 new sales for a grand total of 25,300 new sales.

We can arrive at the same answer using marginal analysis. Total SpentSales from TV ads Sales from Radio ads Marginal Impact of TV ads Marginal Impact of radio ads $000 $100,0004, $200,0009,0001,800 $300,00012,7502,550 $400,00016,0003,200 $500,00018,7503,750 $600,00021,0004,200 $700,00022,7504,550 $800,00024,0004,800 $900,00024,7504,950 $1,000,00025,0005,000 Calculate the marginal impact of an additional $100,000 of spending. = change in sales / change in spending

Total SpentSales from TV ads Sales from Radio ads Marginal Impact of TV ads Marginal Impact of radio ads $ $100,0004, $200,0009,0001,800 $300,00012,7502,550 $400,00016,0003,200 $500,00018,7503,750 $600,00021,0004,200 $700,00022,7504,550 $800,00024,0004,800 $900,00024,7504,950 $1,000,00025,0005,000 Marginal Impact = change in sales / change in spending

Total SpentSales from TV ads Sales from Radio ads Marginal Impact of TV ads Marginal Impact of radio ads $ $100,0004, $200,0009,0001,800 $300,00012,7502,550 $400,00016,0003,200 $500,00018,7503,750 $600,00021,0004,200 $700,00022,7504,550 $800,00024,0004,800 $900,00024,7504,950 $1,000,00025,0005,000 Marginal Impact = change in sales / change in spending Suppose you are spending $900,000 on TV. Should you spend the remaining $100,000 on TV or radio?

Total SpentSales from TV ads Sales from Radio ads Marginal Impact of TV ads Marginal Impact of radio ads $000-- $100,0004, $200,0009,0001,800 $300,00012,7502,550 $400,00016,0003,200 $500,00018,7503,750 $600,00021,0004,200 $700,00022,7504,550 $800,00024,0004,800 $900,00024,7504,950 $1,000,00025,0005, Marginal Impact = change in sales / change in spending Suppose you are spending $900,000 on TV. Should you spend the remaining $100,000 on TV or radio?

Total SpentSales from TV ads Sales from Radio ads Marginal Impact of TV ads Marginal Impact of radio ads $000-- $100,0004, $200,0009,0001,800 $300,00012,7502,550 $400,00016,0003,200 $500,00018,7503,750 $600,00021,0004,200 $700,00022,7504,550 $800,00024,0004,800 $900,00024,7504,950 $1,000,00025,0005, Marginal Impact = change in sales / change in spending Suppose you are spending $900,000 on TV. Should you spend the remaining $100,000 on TV or radio? radio

Total SpentSales from TV ads Sales from Radio ads Marginal Impact of TV ads Marginal Impact of radio ads $000-- $100,0004, $200,0009,0001,800 $300,00012,7502,550 $400,00016,0003,200 $500,00018,7503,750 $600,00021,0004,200 $700,00022,7504,550 $800,00024,0004,800 $900,00024,7504,950 $1,000,00025,0005, Suppose you are spending $800,000 on TV and $100,000 on radio. Should you spend the next $100,000 on TV or radio?

Total SpentSales from TV ads Sales from Radio ads Marginal Impact of TV ads Marginal Impact of radio ads $000-- $100,0004, $200,0009,0001,800 $300,00012,7502,550 $400,00016,0003,200 $500,00018,7503,750 $600,00021,0004,200 $700,00022,7504,550 $800,00024,0004,800 $900,00024,7504, $1,000,00025,0005, Suppose you are spending $800,000 on TV and $100,000 on radio. Should you spend the next $100,000 on TV or radio?

Total SpentSales from TV ads Sales from Radio ads Marginal Impact of TV ads Marginal Impact of radio ads $000-- $100,0004, $200,0009,0001, $300,00012,7502,550 $400,00016,0003,200 $500,00018,7503,750 $600,00021,0004,200 $700,00022,7504,550 $800,00024,0004,800 $900,00024,7504, $1,000,00025,0005, Suppose you are spending $800,000 on TV and $100,000 on radio. Should you spend the next $100,000 on TV or radio? radio

Total SpentSales from TV ads Sales from Radio ads Marginal Impact of TV ads Marginal Impact of radio ads $000-- $100,0004, $200,0009,0001, $300,00012,7502,550 $400,00016,0003,200 $500,00018,7503,750 $600,00021,0004,200 $700,00022,7504,550 $800,00024,0004,800 $900,00024,7504, $1,000,00025,0005, Suppose you are spending $700,000 on TV and $200,000 on radio. Should you spend the next $100,000 on TV or radio?

Total SpentSales from TV ads Sales from Radio ads Marginal Impact of TV ads Marginal Impact of radio ads $000-- $100,0004, $200,0009,0001, $300,00012,7502,550 $400,00016,0003,200 $500,00018,7503,750 $600,00021,0004,200 $700,00022,7504,550 $800,00024,0004, $900,00024,7504, $1,000,00025,0005, Suppose you are spending $700,000 on TV and $200,000 on radio. Should you spend the next $100,000 on TV or radio?

Total SpentSales from TV ads Sales from Radio ads Marginal Impact of TV ads Marginal Impact of radio ads $000-- $100,0004, $200,0009,0001, $300,00012,7502, $400,00016,0003,200 $500,00018,7503,750 $600,00021,0004,200 $700,00022,7504,550 $800,00024,0004, $900,00024,7504, $1,000,00025,0005, Suppose you are spending $700,000 on TV and $200,000 on radio. Should you spend the next $100,000 on TV or radio? TV

We can arrive at the same answer using constrained optimization. max B = f(T, R) s.t. $1,000,000 = T + R {T, R} new beer sales need to know functional relationship constraint