Question

Please show all work.

Problem #5: Cross-price elasticity Consider teenage labor and adult labor as separate inputs in production for fast-food restau- rants. Suppose the wage of teenage workers increases (but the adult wage remains the same). Analyze the effect of the teenage wage increase on fast-food restaurants' employment of adult labor, given that: 1. Teenage labor costs are a large share of total costs at fast-food restaurants. 2.Adults dislike the tasks teenagers do at fast-food restaurants (i.e. cleaning bathrooms), so it takes big increases in their wages to get them to do this kind of work. Given these 2 facts, are teenage workers and adult workers more likely to be gross substitutes or gross complements in fast-food production, holding all other factors constant? Explain your answer.

Answer 1

In the given case , teenage workers and adult workers are mere substitutes. This is because if the wage of the teenage workers increases , employment of teenage workers will decrease. As such, demand for adult workers will increase which will thereby increase the employment of adult workers. Here, cross-price elasticity can be defined as increase in employment of adult workers due to increase in wages of teenage workers. As both numerator and denominator values are positive , cross-price elasticity is also positive. Positive value of cross-price elasticity is only seen in cases of substitutes . Hence, it is confirmed that adult workers and teenage workers are substitutes.