Cultural goods creation, cultural capital formation, provision of cultural services and cultural atmosphere accumulation

Abstract

The cultural atmosphere in a society is accumulated over time through the consumption of cultural services and is diminished through depreciation. Using cultural capital (e.g., cultural heritage, paintings, music scores), cultural services are provided by the cultural-services industry (e.g., museums, opera houses); cultural capital is enlarged by new cultural goods created by individuals. Individuals’ utilities are positively affected by the cultural services they consume, by the cultural goods they create and by the cultural atmosphere and the cultural capital accumulated in society. In a laissez-faire economy, individuals tend to ignore the positive external effects of their cultural-services consumption and creation of cultural goods on other individuals via accumulating cultural atmosphere and cultural capital. Consequently, suboptimally little cultural atmosphere and cultural capital will be accumulated. The efficient intertemporal allocation can be restored by introducing an appropriate subsidy that not only stimulates consumers’ demand for cultural services and the creation of new cultural goods but also enhances the accumulation of cultural atmosphere and cultural capital.

Appendices

Appendix A: Derivation of the marginal conditions of Eq. (14)

The FOCs of Eq. (14) are as follows

$$\frac{\partial H}{\partial g_c}=n_c U_{g_c}-n_c\lambda_{gc}=0,$$

(A.1)

$$\frac{\partial H}{\partial g_s}=n_s\lambda _s S_g -n_s \lambda_{gs}=0,$$

(A.2)

$$\frac{\partial H}{\partial k_c}=n_c U_{k_c}+n_c \lambda _v V_{k_c} -n_c\lambda_k =0,$$

(A.3)

$$\frac{\partial H}{\partial r_s }=n_s\lambda _s S_r -n_s \lambda_r =0,$$

(A.4)

$$\frac{\partial H}{\partial r_v }=n_c\lambda _v V_r -n_c \lambda _r =0,$$

(A.5)

$$\frac{\partial H}{\partial r_y}=\lambda_y Y_r -\lambda_r =0,$$

(A.6)

$$\frac{\partial H}{\partial s_c}=n_c U_s +n_c\mu _k -n_c\lambda_{sc} =0,$$

(A.7)

$$\frac{\partial H}{\partial s_s}=-n_s \lambda_s +n_c n_s \lambda _{sc} =0,$$

(A.8)

$$\frac{\partial H}{\partial v_c }=n_c U_v +n_c \mu_g -n_c \lambda _v =0,$$

(A.9)

$$\frac{\partial H}{\partial y}=-\lambda_y +\lambda_c =0,$$

(A.10)

$$\frac{\partial H}{\partial y_c}=n_c U_y -n_c \lambda_c =0,$$

(A.11)

$$\dot{\mu}_g =\delta \mu_g -\frac{\partial H}{\partial g}= \delta\mu _g+\alpha _g \mu_g -n_c\lambda_{gc}-n_s \lambda_{gs} ,$$

(A.12)

$$\dot{\mu}_k =\delta\mu_k -\frac{\partial H}{\partial k}=\delta \mu_k+\alpha_k \mu_k -n_c \lambda_k .$$

(A.13)

Appendix B

Derivation of Eq. (15)

Taking (A.5): λ _v = λ _r /V _r , (A.6): λ _r = λ _y Y _r , (A.10): λ _y = λ _c and (A.11): λ _c = U _y into account, (A.9): U _v + μ _g −λ _v = 0 can be rearranged to μ _g = (U _y Y _r )/V _r −U _v , or, equivalently as (15): μ _g /(U _y Y _r ) = 1/V _r −U _v /(U _y Y _r ).

Derivation of Eq. (16)

Setting (A.9): μ _g = (U _y Y _r )/V _r −U _v , (A.1): λ _gc = U _{g_c} , (A.2): λ _gs = λ _s S _g , (A.4) and (A.6): λ _s = U _y Y _r /S _r into (A.12): ${\dot {\mu}_g =\left({\delta +\alpha _g}\right)\mu _g -n_c \lambda _{gc}-n_s\lambda_{gs}}$, after some rearrangements in terms to get

$$ \dot {\mu }_g =\left( {\delta +\alpha _g } \right)\left( {\frac{1}{V_r }-\frac{U_v }{U_y Y_r }} \right)-n_c \frac{U_g }{U_y Y_r }-n_s \frac{S_g }{S_r}, $$

or, equivalently, Eq. (16).

Appendix C: Derivation of the marginal conditions of Eq. (25)

$$\frac{\partial H^C}{\partial g_c}=U_g-\beta_c p_{gc}=0,$$

(C.1)

$$ \frac{\partial H^C}{\partial k_c}=U_k +\beta_{vc} V_k-\beta_c p_{kc} =0, $$

(C.2)

$$ \frac{\partial H^C}{\partial r_v}=\beta_{vc}V_r -\beta _c p_r=0, $$

(C.3)

$$ \frac{\partial H^C}{\partial s_c}=U_s +\beta_S -\beta_c p_{sc}=0, $$

(C.4)

$$ \frac{\partial H^C}{\partial s_{cK}}=-\beta_S +\beta_c p_{sK}=0, $$

(C.5)

$$ \frac{\partial H^C}{\partial v_c}=U_v -\beta_{vc}+\beta_c p_v=0, $$

(C.6)

$$ \frac{\partial H^C}{\partial y_c}=U_y-\beta_c p_y =0. $$

(C.7)

Appendix D: Derivation of the marginal conditions of Eq. (27)

$$\frac{\partial H^Y}{\partial y}=p_y -\beta_y=0,$$

(D.1)

$$\frac{\partial H^Y}{\partial r_y}=-p_r +\beta_y Y_r=0.$$

(D.2)

Appendix E: Derivation of the marginal conditions of Eq. (29)

$$\frac{\partial H^S}{\partial g_s}=-p_{gs}+\beta _{sj}S_g=0,$$

(E.1)

$$\frac{\partial H^S}{\partial r_s}=-p_r+\beta _{sj}S_r=0,$$

(E.2)

$$\frac{\partial H^S}{\partial s_s }=p_s-\beta_{sj}=0.$$

(E.3)

Appendix F: Derivation of the marginal conditions of Eq. (31)

$$\frac{\partial H^G}{\partial g_G }=p_g -\beta _G =0,$$

(F.1)

$$\frac{\partial H^G}{\partial v_G }=-p_v +\varphi _g =0,$$

(F.2)

$$ \dot {\varphi }_g =\delta \varphi _g -\frac{\partial H^G}{\partial g}=\left( {\delta +\alpha _g } \right)\varphi _g -\beta _G =\left( {\delta +\alpha _g } \right)p_v -p_g . $$

(F.3)

Appendix G: Derivation of the marginal conditions of Eq. (33)

$$\frac{\partial H^K}{\partial k_K}=p_k-\beta_K =0,$$

(G.1)

$$\frac{\partial H^K}{\partial s_K}=-p_{sK}+\varphi_k =0,$$

(G.2)

$$ \dot{\varphi}_k =\delta\varphi_k-\frac{\partial H^K}{\partial k}=\left({\delta +\alpha _k}\right)\varphi_k-\beta_K =\left( {\delta +\alpha _k} \right)p_{sK}-p_k. $$

(G.3)