A model explaining cultural consumption

4.2A model explaining cultural consumption

Following Lévy-Garboua and Montmarquette (1996) a simple model explaining the demand for cultural events can be formulated. In the framework defined by Stigler and Becker (1977) the culture capital is a combination of initial culture capital and past cultural goods consumption. The model assumes that cultivation of taste to be developed with the earlier consumption experiences, i.e. a model with learning by consuming. There are two goods n₁ and n₂. The first one (n₁) presents the consumption of performing arts and the second (n₂) the consumption of sport events. The arguments of the intertemporal utility function are the periodic partial utilities, which takes the form u(s_1tn_1t, s_2tn_2t) in which n_it ≥ 0 and s_it signifies the subjective qualities anticipated before the actual consumption decision. The subjective quality of each good and for each consumer depends on previous personal consumption experiences of them. The expectations are individual: s_iτ^t-1 = E_t-1(s_iτ) represents the subjective quality of good i expected by the consumer for the forthcoming period τ (τ = t, …, T) conditional on the knowledge in t-1.

(4-1) s_it = s_it^t-1 + ε_it

if n_it > 0 and a pleasant or unpleasant surprise takes place by comparison with expectations: E_t-1(ε_it) = 0. Every new experience of a given cultural event (performing art or sport event) reveals to the consumer an unexpected positive or negative revision in her taste for it. After this experience, the consumer assesses her expectations in an adaptive manner with assuming a loss of knowledge by forgetting at a constant rate δ_i > 0:

(4-2) s_i,t+1^t = (1- δ_i)([1-m_i)s_it^t-1 + m_is_it] = (1- δ_i)[s_it^t-1 + m_i ε_it]

where 0 < m_i < 1 is the likelihood attached to the results of the latest experience. Expectations in (t-1) for all forthcoming periods are then:

(4-3) s_iτ^t-I = (1- δ_i)^τ-ts_it^t-1.

The consumption decisions taken in t are thus based on the following intertemporal, additive utility function

(4-4)

where represents the expected consumption quantities and is the discount factor. The consumer maximises expected long-range utility subject to

(4-5)

where W_t represents wealth (and other than cultural consumption) at t, Y_t is the labour income at t, p_i is the price of the good i, and n_i stands for the quantity demanded for cultural event (n₁) or sport event (n₂). Under the assumption that the consumer can borrow and lend freely, the intertemporal optimality conditions for expected utility maximisation are:

(4-6) and λ_t = E_t{(1+r)λ_t+1}

where is the marginal utility of the ith good at time t and λ_t is the expected value of marginal utility of wealth at t. The solution gives the Frisch demand (constant marginal utility for wealth) demand functions for n₁ and n₂:

(4-7) n_it = f_it(p_1t, p_2t, λ_t).

If the marginal utility for wealth is invariable over time, it could be linked to socioeconomic variables, like the gender, age and education. With a decreasing marginal utility of wealth, the consumption of art is more likely to be a luxury the lower the level of wealth. The Frisch demand is convenient since under the assumption of additivity in utility function, the quantities purchased are characterised in terms of goods’ prices to the price of utility (Browning, Deaton and Irish 1985). Such demands should be distinguished from the usual Marshallian (uncompensated) demands that relate quantities demanded to prices and expenditure or form the Hicksian (compensated) demands that relate quantities demanded to prices and utility. If good’s prices change the Frisch demand is such that consumers are money compensated until the price of utility returns to its original value. The individual qualities depend on the consumer’s previous experiences. The Frisch demand functions are suitable to explain cultural consumption since those consumers that interrelate attendance with high quality will have a low personalised price (Seaman 2006, 445). The taste for cultural and sport events is generated by culture specific capital. Individuals differ widely in their taste for specific art forms. Some like performing arts while others prefer sport events. The intertemporal utility function is conditional on past consumption. If there is no learning process, the accumulated experience remains constant and there is no dynamic formulation. The model is strongly based on the assumption that accumulated experience including the initial culture capital determines the future consumption, however, even person with the same utility function and the same wealth may have different culture consumption behaviour if they have different experiences. The accumulation function is connected to human specific variables, like the formal education. The Frisch demand is suitable here, since over the life-cycle consumers have different socio-economic background. The intertemporal additivity assumption allows decentralisation over time or age. Each period of time is regarded as a slice of life and lifetime utility is the sum of all slices.

The Eurobarometer 56.0 survey (Table 4-2) shows that there is a reverse relationship in cultural consumption with age. Elder seem to favour classical concerts while younger are more often sport lovers.

On the basis of preliminary statistical examination and based on earlier studies a hypothesis can be set:

H1: Cultural consumption of performance art and sport is heavily dependent on the gender, person’s age and education. Furthermore, the regional supply has an effect.
Both the consumer’s incomes and the prices of the cultural events are not used as explanatory variables since the prices are not known and since incomes are associated with gender, age and education (e.g. Asplund 2008).
In the Helsinki metropolitan area there are more visitors than elsewhere. Women go more often than men. The audience composition of the theatrical or opera performances and classical music concerts is different than that of the sport events. Moreover the composition of sport spectators also depends on gender, person’s age and education but in contrast to the performing arts audiences. The second hypothesis is set:

H2: The sport events and performance arts are substitutes or exclusionary.