The kinked demand curve model

Overview

Demand curve elastic above the kink, demand curve inelastic below the kink and discontinuity in marginal revenue.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   What behavioural assumption about rivals lies behind the kinked demand curve model?

   Model answer

   The model assumes asymmetric reactions: if the firm cuts its price, rivals match the cut to protect their market share, but if the firm raises its price, rivals leave their own prices unchanged and let it lose customers to them.

2. 2

   Where does the kink in the kinked demand curve sit?

   Model answer

   The kink sits at the firm's current price and current output, the point at which it is presently trading. The model takes that point as given and explains why the firm stays there, so the kink is located by the prevailing price rather than derived from anything else in the model.

3. 3

   Describe the kinked demand curve diagram precisely enough for someone to redraw it.

   Model answer

   Price per unit is on the vertical axis and quantity of output per period on the horizontal axis. Draw a demand curve that is a shallow, relatively flat line coming down from the left; at the current price and output it bends sharply and continues to the right as a much steeper line. That bend is the kink. Above the kink the demand curve is relatively price elastic, below it relatively inelastic. Now draw the marginal revenue curve: for the flat upper segment draw a line starting at the same vertical intercept but falling twice as steeply, and stop it directly below the kink. For the steep lower segment draw a second marginal revenue line, also twice as steep as its own demand segment, and start it directly below the kink at a much lower level. The two pieces do not meet, so at the kink output there is a vertical gap in the marginal revenue curve, conventionally shown as a dashed vertical line. Finally draw an upward-sloping marginal cost curve that passes through the interior of that gap.

4. 4

   Why is the demand curve elastic above the kink?

   Model answer

   Above the kink the firm has raised its price and rivals have not followed, so its product is now dearer than close substitutes that are otherwise identical in price. A large number of customers switch away for a small price rise, so the proportionate fall in quantity demanded exceeds the proportionate rise in price and demand is price elastic.

5. 5

   Why is the demand curve inelastic below the kink?

   Model answer

   Below the kink the firm has cut its price and rivals have matched it, so relative prices across the market are unchanged and the firm wins almost no customers from its competitors. The only extra sales come from the small expansion of the whole market as the general price level falls, so quantity demanded rises very little for a large price cut and demand is price inelastic.

6. 6

   A firm currently sells 12 units at £76. Above that price its demand is given by P = 100 - 2Q and below it by P = 172 - 8Q. Confirm that both segments pass through the current position and calculate the price elasticity of demand on each.

   Model answer

   On the upper segment, 100 - 2 × 12 = 100 - 24 = £76, and on the lower, 172 - 8 × 12 = 172 - 96 = £76, so both pass through 12 units at £76. On the upper segment a £1 fall in price raises quantity by half a unit, so elasticity is -(1/2) × (76/12) = -3.17, which is elastic. On the lower segment a £1 fall raises quantity by an eighth of a unit, so elasticity is -(1/8) × (76/12) = -0.79, which is inelastic. The asymmetry in rivals' reactions is what produces the difference.

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